Based on the ideas of Karl Marx and Friedrich Engels, communism seeks the liberation of the working class, the "proletariat" from the oppressive chains of the capitalists, the "bourgeoisie", by rallying the proletariat to join together and overthrow the capitalist-run governments of the world. After this revolution, the people would not be governed by superiors but guided by a committee of their peers. The class system as it existed in most countries was to be eliminated, putting every member of a communist state on the same social and economic level. In capitalist countries, especially the United States, we're taught from a young age that communism is oppression. However, increased literacy, life expectancy, quality of life, advances in science and technology and healthcare, and the abolition of slave labor, are all achievements of communist countries throughout the world. Many opinion polls show people living in formerly communist countries show people believing life was better under communism, and the younger generation in these countries also have nostalgia for the communist past that they've never even experienced.
For a good starting point on communism, try Albert Einstein's article Why Socialism?
From the post-WWI era to the early nineties, the conflict between capitalism and communism radically shaped the face of politics and economics, and social spheres were directly or indirectly influenced in one way or another by the communists. The Western world, and especially America, were strongly opposed to the spread of communism, as it was the antithesis of the heavily capitalist system favored in the United States in particular, which was a direct cause not only of the Cold War but also the various wars that America waged during the heyday of communism (1922-1991), especially those in Korea (1950-53) and Vietnam (1955-1975). Fear of communism in America reached a fever pitch in the 1950s with the actions of Joseph McCarthy and his House Un-American Activities Committee, as well as the anti-communist actions of the FBI under J. Edgar Hoover. However, hatred for the ideology still runs deep in that country, and tension between the two major players in the Cold War still exists to this day, despite the collapse of Russian communism in 1991 under the government of Mikhail Gorbachev. Communism and communists became and remained popular villains because of the enduring distrust felt by America, and were essentially replacements for the Nazis as stock villains throughout the Cold War, and many remained after.
Famous Communist leaders include Vladimir Lenin and Joseph Stalin of Russia, Mao Zedong of China, Fidel Castro of Cuba and Josip Broz Tito of Yugoslavia.