Well, this is a very complicated and in-depth question, that deserves a book and not a single line. Basically, it was a war of ideologies; Capitalism vs Communism. The United States and the Soviet Union both wanted to spread their influences, which created tension between the two powers. This tension was further augmented by the fact that both sides had a large nuclear arsenal, although the possession of nuclear weapons may have been the factor that negated an all out war between the powers. However, you can see conflicts where the sides backed opposing parties, such as that in Vietnam (Wher the capitalist South was backed by the United States and later US troops, and the communist north by The Soviet Union and ally Communist China. You can see other examples of this in Cuba, and the middle east throughout the cold war.