Communism is a political and economic theory, originated by Karl Marx and Friedrich Engels, that proposed class struggles in history would end with the people governing themselves and living cooperatively in a society where all would share together equally. "From each according to his ability, to each according to his needs," Marx had written in Critique of the Gotha Program (1875). In actual practice, communist society had to be imposed by government from the top in the places where it came into power, such as the Soviet Union and China.
The USA and USSR were embroiled in a Cold War because of their radically different worldviews -- the USA believing in capitalism and promoting democracy, the USSR adhering to communism and governing in an authoritative, totalitarian manner. Both sides believed the other would try to encroach against their way of life, and the tensions of the Cold War (along with military buildup and arms races) were the result.
Containment policy was recommended by US diplomat George F. Kennan, who believed there were enough internal contradictions and problems in the Soviet system that it could not sustain itself long-term. So he recommended (and America followed) a practice of keeping the Soviet Union in check, containing the spread of communism, rather than going on direct attack vs. the USSR.
