What is free-market capitalism?  Let's start with some basic definitions of the component parts of that phrase...

Free -- adj. Not imprisoned, controlled, governed, dependent, restrained, or subject to interference.  The basic foundation of freedom is self-ownership.  Nobody else has a higher claim on you than you do.  You have total control and veto power over what may be done to you or requested of you by others. 

Market -- n. A place, gathering, region, or opportunity for exchanging goods and services.  A free market is one where exchanges are done entirely voluntarily, under no external force or duress.  Whether an exchange occurs is entirely dependent on whether the parties to the transaction believe it is in each of their best interests.  For instance, a dairy farmer may have lots of milk, but no bread, whereas the baker may have lots of bread, but no milk; milk is more valuable to the baker than the farmer because he has no milk, and bread is more valuable to farmer than the baker because he has no bread; so the two may exchange milk for bread and bread for milk, each coming away wealthier and better off than before the transaction.  They feel no remorse over what has transpired and would gladly do it again, and probably will.  A free-market hallmark is the double thank-you.  The baker thanks the farmer for the milk while the farmer simultaneously thanks the baker for the bread.  If an exchange is not free, but coerced, then one side leaves better off and the other worse off.  You don't thank your tax collector, for example. 

Capital -- n. An asset, advantage, marketable skill, or other form of wealth which can be employed in the production of goods and services.  To continue our example, the dairy farmer would consider his farm, his animals, his milk bottles, his knowledge, and his labor as capital.  He uses them to produce dairy products.  The baker would consider his bakery, his oven, his stores of flour and other ingredients, his relationship with his suppliers, his knowledge, and his labor as capital.  Without capital, neither the farmer nor the baker could produce their goods.  There would be no milk and no bread. 

Capitalism -- n. An economic system in which the means of production are privately owned and operated.  What this means is that the farmer owns his land and cows and bottles and his own labor and expertise.  Likewise, the baker owns his shop and oven and supplies and proprietary connections and his own labor and expertise.  He is not an indentured servant or a slave or an employee of someone else, namely the government.  This is contrasted with socialism/communism where the means of production are owned by the State.  Under capitalism, the farmer and the baker invest the profits of running their business into the purchase of more capital in order to expand their operations and produce even more goods, if there is a market for them, or they may invest in ancilliary lines of business such as ice cream and pastries, if there is a better market for those goods.  Supply and demand are the main arbiters of how future production should be best utilized.  This was referred to by Adam Smith as the "invisible hand" of the market, whereby the self-interest (profit-motive) of producing the goods in highest demand or filling unmet niches tends to produce the highest collective good for society.  Under socialism, the farmer and the baker only earn a wage and the State decides how capital should be best managed, usually for political reasons, independent of any market forces.  Under socialism, the "invisible hand" of the market is ignored and thus capital is usually malinvested, producing supply shortages in some sectors, surplusses and waste in others, and unmet expectations all around. 

Free-market capitalism then is an economic system where the means of production are privately owned and operated and the markets for goods and services are not restrained or controlled by outside forces.  Individuals own themselves and the fruits of their labor, including the ability to amass capital in order to support their future production.  Individuals guide all of their own productive activities without coersion and offer up their goods and services for voluntary exchange.  Individuals are free to accept or reject any offer in the marketplace according to their own judgement.  There are no limits or terms placed upon them by the State.  Free-market capitalism is the de facto economic system in the absense of a government, and always has been.  Unless an external structure is placed upon them, people naturally act according to free-market capitalist princples.  It is a most natural form of human cooperation which maintains a fair and equitable balance of rewards achieved versus work and skill applied.  For instance, as noted, the baker and the dairy farmer are both better off when they agree to trade with each other than if they did not.  It provides them with a division of labor whereby both men don't have to try to both bake bread and raise dairy cows.  They can concentrate on their most finely-honed trade but still enjoy the products of the other.  And if the baker is lazy and only produces enough bread to buy his milk and feed his family, then his rewards are proportional to his efforts.  Perhaps he enjoys painting or playing sports or sleeping instead of working harder than that.  Those are his values and his choices.  The dairy farmer may have other goals however, and he may put in long hours and develop a line of cheeses and yoghurt and maybe franchise his operations by investing in another farm run by an apprentice.  The dairy farmer may therefore reap the rewards of his hard work and skill and become quite wealthy.  In exchange for his wealth and what it can buy, he has given up the ability to enjoy painting or playing sports or sleeping long hours in the meantime.  The result in each case is fair and equitable. 

The proper role of government in a free-market capitalist system is to prevent fraud, force, or theft only, and not to otherwise influence voluntary commerce.  For instance, the government should act to prevent or punish the baker from stealing milk from the dairy farmer, delivering day-old bread to the farmer when the agreement was for fresh bread, or blackmailing the farmer over an embarrassing incident he doesn't want to be publicly known in order to get a special deal on his milk.  But the government should not dictate that the baker may only charge a maximum of one loaf of bread per gallon of milk, as that is something for the baker and farmer to work out between each other, based on their own individual values and governed largely by supply and demand.  Nor should the government dictate the technique the farmer uses to milk his cows or the recipe the baker must use to make his bread.  And the government certainly should not force the baker to license his oven or the farmer to register his cows.  When the government starts interfering with capital, production, and transactions in this fashion, it is no longer free-market capitalism.  When the government uses its monopoly on the legal use of force to govern capital, production, or transactions, the government has made a claim on the capital and the individuals which is above their own claim.  They are no longer free, but in a way enslaved.  This is a form of socialism, though it is generally considered a "mixed economy" or some form of regulated capitalism, such as merchant capitalism or feudalism or national socialism, where the State maintains the highest claim and veto power, but acts as though individuals or groups have ownership or at least guardianship so as to avoid the extreme inefficiency of complete centralized planning. 

Above, I noted that free-market capitalism is a form of cooperation.  This may seem contradictory to a popularly recognized element of capitalism: competition.  But it should be recognized that competition and cooperation are not mutually exclusive in an economic system.  Competition arises when there is more than one producer of a particular good or service.  For instance, in our ongoing example, a second baker may move into town.  Now, where before the original baker had a monopoly on the production of bread, he now has a competitor.  The second baker will compete by either producing a higher quality bread, a different kind of bread, or charging a lower price for his bread.  Any of these things -- better quality, more diversity, or lower prices -- are all good things.  As long as Baker1 doesn't react by competing with Baker2 on one or all of these fronts, most of Baker1's customers will instead choose to buy bread from Baker2.  Baker2 may then react to this surge in demand by raising prices, driving some customers back to Baker1 again.  The voluntary transaction between producer and customer is a form of cooperation.  They are each better for it.  But the competition between multiple producers makes the deal a customer receives much better or at least broadens their choices.  So, where the dairy farmer before was pleased to get bread in exchange for his milk, he now has the option of expensive sweet bread and cheaper sourdough bread.  And as time goes on, competition may have the bakers innovating such things as sliced bread!  Therefore, competition is a very important part of free-market capitalism, as it drives innovation and efficiency.  In contrast, there is no motivation to innovate or improve efficiency under a socialist system because there are no independent proprietors who reap the rewards of their commerce.  Under socialism, innovation and efficiency can only be driven by State mandate, which is why products in socialist economies are only developed to the point that they are good enough, and no further.  The result is things like the East German Trabant, a notoriously small, dirty, ugly, poorly-performing automobile that remained largely unchanged for 30 years. 

Free-market capitalism drives cooperation of other kinds as well, however.  As I have already suggested above, perhaps the farmer is unsatisfied with the scale of his operation and wishes to expand.  However, the farmer cannot manage two properties by himself.  So, he cooperates with his apprentice, who wants to open his own dairy.  In exchange for the up-front capital that the farmer invests as well as his ongoing expertise and support, the apprentice will pay the farmer a percentage of the profits of the new operation.  This might be considered a franchise or a partnership arrangement.  Another form of cooperation is raising lots of capital from many investors in order to engage in some new venture.  Let's say that the people of our imaginary town are unhappy with the monopoly pricing of the dairy farmer.  They believe that if they owned a dairy, they could produce milk at better quality and cheaper prices.  But none of them have enough resources to open a dairy on their own.  So what they do is form a corporation which is composed of a number of shares of stock.  One person may only have very limited resources and therefore only buy a few shares, while his neighbor may be relatively wealthy and buy many shares.  As a result, they can both participate in the new business, but their voting control over what the business does as well as the share of the profits that they receive will be directly proportional to the amount they originally invested (and put at risk for loss if the venture failed).  It's all very fair and equitable.  If it wasn't, they wouldn't agree to it.  Under a free market, nobody is twisting anyone's arm to participate or not.  So, under this cooperative structure called a corporation, many people are able to now fund a business which brings competition to their dairy market.  If, as they expected, they are able to operate more efficiently, they will sell their milk and cheese and yogurt at a lower price and force the original dairy farm to either lower prices or improve quality or otherwise compete with them.  And this competition drives continuing innovation and efficiency.  And continually increasing efficiency drives economic growth by freeing up capital and labor to pursue new ventures. 

In this light, I think everyone can agree that free-market capitalism seems like a pretty good system.  It is voluntary, fair, equitable, efficient, and produces innovation and growth.  So, why have various movements over the centuries challenged free-market capitalism?  The primary enemies of free-market capitalism are those who do NOT want it to be voluntary or fair or equitable or efficient or innovative or growing.  What possible motivations could people have for this?

• Repressive political regimes do not want commerce to be voluntary because it reduces their ability to coerce the People.
• Religious organizations and luddites do not want innovation because they fear it will make them irrelevant.
• The poor do not like that capitalism is equitable because they are envious of what others have been able to accumulate.
• The rich are against its fairness because they want to maintain any advantages that they may have created or been born into.
• Environmentalists hate the growth that capitalism creates because they see people as a plague upon the planet.
• Busy-bodies don't like capitalism because it's voluntary, and they want to dictate how everyone else behaves.
• Sentimentalists don't like the efficiency of production because they value the old-style craftsmanship.
• Lazy and undriven people do not like the equitable nature of capitalism, for they want to benefit from others' hard work.
• Meek and ignorant people don't trust their own judgement to make good voluntary choices and thus want everything regulated.
• Spiritualists feel like the profit-motive which drives capitalism is too materialist and spiritually impure.
• Some rich people feel guilty about having things that others don't, and thus want to disperse (other people's) capital more equally, but clearly unfairly and inequitably.
• Et cetera.  I'm sure the list could go on and on. 

Are any of these valid criticisms of free-market capitalism?  I don't think so.  From a moral perspective, nobody should ever have a higher claim over you and the fruits of your labor than you yourself have.  Some people point out that we have a moral obligation to help those who are less fortunate.  There may be some truth to that.  However, that is entirely outside of the scope of the economic system.  That's why charity has always been an individual or religious matter.  No matter how needy someone may be, they do not have an inherent claim on you or your labor that is above your own.  Only you can decide to voluntarily give of yourself and your capital.  The needy do not have a right to steal it.  And governments do not have a right to steal it in their name.  Charity must be voluntary.  And if people tend to value the truly needy less than their own luxuries, then that is a horrible testament to the people who allow it to occur, but I know of no society in which that has ever been the case.  There have always been half-way houses and soup kitchens and hand-outs to beggars.  The charity is there for all who need it.  It may not be a pleasant or comfortable life to depend solely on charity, but then it really shouldn't be.  To elevate the non-working destitute to a level of comfort higher than the hard-working would be counter-productive.  Everyone deserves a second chance to pull themselves up by the bootstraps, and there is plenty of charity for that purpose.  But nobody should live comfortably off of charity alone.  A natural human sense of sympathy tends rightly to end as soon as it's clear that someone is taking advantage of it. 

What about the view that some have lately that corporations are evil enterprises only interested in profits no matter the harm they may cause?  Well any individual or organization which causes harm should be prevented from or punished for doing so by the government.  Remember, that is the government's only role in free-market capitalism.  Nothing about the nature of corporations themselves lend to any kind of abuse.  Corporations are democratic structures for the voluntary cooperation of many individuals to achieve a larger objective and to reap the rewards of such in an equitable fashion.  To the extent that certain corporations may become dominated by particularly ruthless stockholders and engage in harmful activity with the blessing of government, it is a failing of government, not of free-market capitalism.  The main thing to remember in regard to government is that government is a necessary evil and a powerful tool which needs a constantly vigilent People to prevent its escaping the bounds of its charter.  Government is not a benevolent force which can be trusted with our well-being.  It is a magnet for corruption and tyranny that should only be empowered enough to maintain the rule of just law.  We neglect the advice of our Founding Fathers in this regard at our own peril.  It pains me to constantly see the red herring thrown about that "evil corporations" are the cause of this or that tyranny when the real culprit lies with corrupt government.  The answer to government corruption is NOT to give them more power and more control by relinquishing our sovereign rights over our selves and our property.  The answer to a corrupt government is to strip it of its unnecessary powers and decrease the amount of money that it controls.  Usually the problem is that government has grown too big, has the power to grant too many favors, and controls too much money.  Returning it to the powers delegated in its charter, the Constitution, is the way to solve the abuses of individuals and groups operating under free-market capitalism. 

It should also be pointed out that capitalism is not a political philosophy.  Capitalism can work under any political system which guarantees the freedom of its citizens.  It is usually best practiced for this reason under a constitutional republic, but could also function in a pure democracy or even a benevolent dictatorship, if such a thing were truly possible.  Free-market capitalism becomes very difficult to outright impossible in any situation in which the People are coerced or forced however.  That's why dictatorships, plutocracies, oligarchies, monarchies, theocracies, and other forms of non-popular rule generally result in feudalism, merchantilism, socialism, communism, or mixed economies.  Free markets and free people go hand in hand. 

For more information on free-market capitalism, and some of the fallacies you may have heard (such as that war drives productivity), please read "Economics in One Lesson" by Henry Hazlitt and some of the other books I recommend following this article below.