Imagine you are playing with your friend and both of you have a toy car. You both want to play with the same toy car, but neither of you wants to let go of it. This is what happened between two countries, the United States and the Soviet Union, but instead of a toy car, they wanted control over the world.
After WWII, the Soviet Union had a different way of government, communism, and the United States had a different one, democracy. They both thought that their way of life was better and that they should control the world. However, instead of fighting with weapons, they both tried to show off who was better in other ways.
The United States built a lot of weapons and had a lot of money, so they showed off their power by trying to help poor countries and developing weapons that were more powerful than the Soviet Union's weapons. The Soviet Union also tried to show off by building their own powerful weapons and helping developing countries that were communist.
This competition created a lot of tension between the two countries, and both sides tried to get allies to support them. This also led to a lot of spying and suspicion between the two countries, and both sides were scared that the other country might attack them.
This competition lasted for many years and it was called the Cold War because there was no actual fighting, but there was a lot of tension and fear between the two countries. It finally ended in the early 1990s when the Soviet Union fell apart and the Cold War was over.