What is Capitalism?
Capitalism is a social system based on the principle of individual rights. Politically, it is the system of laissez-faire (freedom). Legally it is a system of objective laws (rule of law as opposed to rule of man). Economically, when such freedom is applied to the sphere of production its result is the free-market.
What is Socialism?
Socialism—defined as a centrally planned economy in which the government controls all means of production—was the tragic failure of the twentieth century. Born of a commitment to remedy the economic and moral defects of capitalism it has far surpassed capitalism in both economic malfunction and moral cruelty. Yet the idea and the ideal of socialism linger on. Whether socialism in some form will eventually return as a major organizing force in human affairs is unknown, but no one can accurately appraise its prospects who has not taken into account the dramatic story of its rise and fall.
Differences?
Capitalism and socialism are somewhat opposing schools of thought in economics. The central arguments in the socialism/capitalism debate are about economic equality and the role of government: socialists believe economic inequality is bad for society and the government is responsible for reducing it via programs that benefit the poor. e.g. free public education, free or subsidized healthcare, social security for the elderly, higher taxes on the rich. On the other hand, capitalists believe that government does not use economic resources as efficiently as private enterprise and therefore society is better off with the free market determining economic winners and losers.
The U.S. is widely considered the bastion of capitalism and large parts of Scandinavia and Western Europe are socialist democracies. However, the truth is every developed country has some programs that are socialist.
sources:
http://www.diffen.com/difference/Capitalism_vs_Socialism
http://capitalism.org/
http://www.econlib.org/library/Enc/Socialism.html