Capitalism is a social system based on individual rights.
Capitalism, according to the greatest defender of capitalism in the 20th-century, Ayn Rand, “is a social system based on the recognition of individual rights, including property rights, in which all property is privately owned.”
The term capitalism is used here in the broader philosophical, political sense (social system), and not in the narrower economic sense (market economy).
Capitalism is not just an economic system (the free market) that can be grafted onto any political structure. Capitalism is an integrated system with specific dependencies. The economy of capitalism — the free market — depends on a specific legal (objective law), political (individual rights), and ethical (rational self-interest) foundation. It is these dependencies that make individuals free not only in their economic affairs but in their personal affairs as well.
What is the ethical basis of capitalism?
Ethically, capitalism is the moral social system as it leaves the individual free to pursue their rational self-interest.
Capitalism is the moral ideal, as it is the only social system that leaves the individual free to be moral — to act by reason in the pursuit of one’s rational self-interest. Such freedom is necessary, writes Ayn Rand,
“Since knowledge, thinking, and rational action are properties of the individual, since the choice to exercise his rational faculty or not depends on the individual, man’s survival requires that those who think be free of the interference of those who don’t. Since men are neither omniscient nor infallible, they must be free to agree or disagree, to cooperate or to pursue their own independent course, each according to his own rational judgment. Freedom is the fundamental requirement of man’s mind.” 
What is the political system of capitalism?
Politically, capitalism is the social system based on the principle of individual rights.
Politically, capitalism is the system of freedom (laissez-faire) that regards the individual as a sovereign being with an inalienable right to their own life (individualism). Capitalism is a social system based on the principle of individual rights, i.e., freedom (from the initiation of physical force). It is to banish the initiation of physical force (and its corollary fraud) from all relationships that governments are instituted.
The recognition of individual rights entails the banishment of physical force from human relationships: basically, rights can be violated only by means of force. In a capitalist society, no man or group may initiate the use of physical force against others. The only function of the government, in such a society, is the task of protecting man’s rights, i.e., the task of protecting him from physical force; the government acts as the agent of man’s right of self-defense, and may use force only in retaliation and only against those who initiate its use; thus the government is the means of placing the retaliatory use of force under objective control.” 
What is the legal system of capitalism?
Legally, capitalism is the objective legal system based on a rule of law under a constitutional republic with a government limited to the protection of individual rights.
Objective control highlights the essential characteristic of capitalism’s legal system. Legally, capitalism is a legal system of clear, unambiguous, objectively defined laws based on the principle of individual rights, i.e., the rule of law (legislation) as opposed to the “rule of man” (regulation). Under such a legal system one is free to act so long as one does not violate the rights of others, i.e., voluntarily.
The government is not a regulator (dictator) but a referee (impartial judge and policeman), i.e., the state is not a master but a paid public servant.
By banning the initiation of physical force (and fraud) from all relationships, capitalism leaves individuals free to regulate their own affairs and freely associate and exchange values with other individuals on a voluntary, peaceful, mutually beneficial basis. It is a contractual (as opposed to a coercive) society. Again quoting Ayn Rand:
“In a capitalist society, all human relationships are voluntary. Men are free to cooperate or not, to deal with one another or not, as their own individual judgments, convictions, and interests dictate. They can deal with one another only in terms of and by means of reason, i.e., by means of discussion, persuasion, and contractual agreement, by voluntary choice to mutual benefit. The right to agree with others is not a problem in any society; it is the right to disagree that is crucial. It is the institution of private property that protects and implements the right to disagree—and thus keeps the road open to man’s most valuable attribute (valuable personally, socially, and objectively): the creative mind.” 
What is the economic system of capitalism?
Economically, capitalism is an economic system based on the principle of individual rights, characterized by a free market in goods, services, and ideas.
Economically, when freedom under the rule of law, under a system that protects the right to private property and the freedom to contract, is applied to the sphere of production and trade, it results in a free market. Under capitalism, there is a separation of economics and state, just like there is a separation of religion and state. What is important to observe is that a free-market is entirely dependent on this specific ethical, political, and legal foundation; without this philosophical foundation, it is only “free” in name. Quoting Ayn Rand:
“In a free economy, where no man or group of men can use physical coercion against anyone, economic power can be achieved only by voluntary means: by the voluntary choice and agreement of all those who participate in the process of production and trade. In a free market, all prices, wages, and profits are determined—not by the arbitrary whim of the rich or of the poor, not by anyone’s “greed” or by anyone’s need—but by the law of supply and demand. The mechanism of a free market reflects and sums up all the economic choices and decisions made by all the participants. Men trade their goods or services by mutual consent to mutual advantage, according to their own independent, uncoerced judgment. A man can grow rich only if he is able to offer better values—better products or services, at a lower price—than others are able to offer.
“Wealth, in a free market, is achieved by a free, general, “democratic” vote—by the sales and the purchases of every individual who takes part in the economic life of the country. Whenever you buy one product rather than another, you are voting for the success of some manufacturer. And, in this type of voting, every man votes only on those matters which he is qualified to judge: on his own preferences, interests, and needs. No one has the power to decide for others or to substitute his judgment for theirs; no one has the power to appoint himself “the voice of the public” and to leave the public voiceless and disfranchised. 
What is the culture of capitalism?
Culturally, capitalism leads to human flourishing, peace, and progress.
Culturally, when such freedom is applied to personal relationships, the arts, technology, and the sciences, it leads to human flourishing, peace, and progress. Again quoting Ayn Rand,
“Capitalism has created the highest standard of living ever known on earth. The evidence is incontrovertible. The contrast between West and East Berlin is the latest demonstration, like a laboratory experiment for all to see. Yet those who are loudest in proclaiming their desire to eliminate poverty are loudest in denouncing capitalism. Man’s well-being is not their goal.” 
In summary: capitalism is the moral (rational-self-interest), political (individualism), legal (rule of law), economic (free-market) social system based on the principle of individual rights that results in peace, progress, and human flourishing. Historically, economically, legally, politically, and morally — in theory and in practice — capitalism is the unknown ideal.
 Ayn Rand “What Is Capitalism?” Capitalism: The Unknown Ideal 19
 Ayn Rand “America’s Persecuted Minority: Big Business” Capitalism: The Unknown Ideal 47
 Ayn Rand “Theory and Practice” Capitalism: The Unknown Ideal 136