Capitalism: an economic system characterized by private or corporate ownership of capital goods, by investments that are determined by private decision, and by prices, production, and the distribution of goods that are determined mainly by competition in a free market. — Merriam Webster Dictionary
First Description: Capitalism was the immediate replacement for feudalism in the Western world. It has existed under many forms of government including the socialist system called communism. As such, it is the dominant economic system in the western hemisphere and, modified slightly, in the eastern hemisphere as well.
It is necessary that the forms in the east and west be slightly different. In the west, capitalism is privately owned capital goods which are used to produce products or services at a profit. These profits are distributed to the investors of that capitalist enterprise. This form can be called laissez-faire capitalism though in reality, most of these entities do have some form of government oversight.
In the east, state capitalism was the norm where the capital goods are owned and directed by the state and profits are distributed, again by the state, to the people. In reality distribution of profits were often less egalitarian.
In essence both the east and west practiced capitalism (the east by necessity to deal with the west) just with different ownership structures.
Second Description: A system of production where a mass of people, otherwise known as productive workers, interact with nature to fashion both a means of production and finished products for human consumption. This system produces a total output greater than the portion of that output paid to the productive workers. This wage portion sustains the workforce by providing for their own consumption and insures their continued productive labor.
This difference between total output and wages, or surplus, is then distributed to the owners of the enterprise, the investors, or both. This arrangement typically involves a contract with the productive laborers such that work is assigned a portion of the surplus in return for work, The contract also stipulates that the space, raw materials, tools, and equipment belong to the company; not the laborers. Finally, the contract stipulates that any surplus beyond the wages paid to labor, are the property of the capitalist enterprise and that surplus is distributed as the enterprise sees fit.