Though the Cold War was never actually a war, the United States and Soviet Union were on the verge of fighting for 50 years. It was a very competitive, competition to see who could be the best, biggest, and strongest nation.
The threat of war being so close between the two nations caused a very significant amount of money being put into the military. It was a question of who was going to attack the other first and they wanted to be prepared.
When the U.S. joined NATO the USSR became angered and got their own allies together to form the Warsaw Pact. The overall purpose of NATO was to help countries come together to defend from communist Soviet Union from spreading.
Once communism made its way to China, American realized that the Soviets ideologies could make there way to America. People in the United States began to become paranoid thinking that everyday people around them could be Soviet spies or support communism.
The U.S. found missiles on cuba that belonged to the Soviet Union. And for thirteen days Americans were scared that they would attack the U.S. and a nuclear war will start. Khrushchev and Kennedy came to an agreement promising that they would get rid of the weapons if the United States promised not to invade Cuba.