Capitalism is free enterprise. Private ownership is allowed and the government can intervene to regulate the economy. It gives people the freedom of choice and the chance to take their own risks, make more mistakes and also succeed and make their own living.
Socialism is where the wealth of the country is devided equally among the people. There are high taxes, but generous public welfare programs.
Communism is where theres a strong central government that controls all industry and plans out the economy. There are not many choices for the individual but the economy can be very strong.