Capitalism is an economic system built on private ownership of the factors of production and their operation for profit. In the capitalist system, private individuals own capital goods, like machinery, and they hire labour (and pay them a wage) to work with this machinery to produce goods for a profit.
In a capitalist economy, decision-making and investment are determined by capitalists in capital and financial markets, whilst prices and distribution are determined by supply and demand and competition in the markets.
The purest form of capitalism is a free market or laissez-faire capitalism. In such a case, private individuals are completely free to choose where to invest, what to produce and what prices to set, without any government interference. Most countries, however, run a mixed capitalist system where private individuals determine most decisions, but there is also some form of government intervention to regulate markets and ensure things such as education, healthcare and other public goods are provided for society.