There were long seeded differences between the United States and the Soviet Union over ideologies. In the Russian Revolution of 1917 the communists took power. The United States and Britain were worried that the same thing might happen in their countries. They thus helped support the White Army, the side against communism, in the Russian Civil War that followed (though they failed). In fact, the United States did not acknowledge the communist government until 1933.
Things had changed temporarily though because Hitler came to power and Stalin and the Soviet Union were redesigned as a kinder people. Although the two sides were able to unite over the common enemy of Germany, after the War people in the United States started to remember their differences.
These differences between the two countries stemmed from their ideologies. Communism was the ideology followed by the Soviet Union. Originally founded by Karl Marx, it said that everything should be owned by the government and then divided up equally among the people who would then all work for it. Not only was the Soviet Union communist, they were totalitarian, meaning all the power was with the rulers.
The United States was capitalist which meant that people could own land and businesses and compete for themselves. This led to a stark contrast between poor and rich. They were also a democracy, which meant it was the people who had a say by electing rulers.
In the Cold War, the division was between these two sides, and there was very little in between.