Why was the Cold War important? I just need a brief but clear explanation.

I will give you two reasons why the Cold War was important.  One has to do with the time when the Cold War was happening.  The other has to do with the way the Cold War ended.

While it was happening, the Cold War was important because it shaped the world.  Essentially every country in the world had to choose whether it was going to side with the US or with the USSR.  The two superpowers tried hard to get countries on their side, giving them aid, but sometimes also creating civil wars within the countries.  Wars like the Korean War and the Vietnam War occurred because of the Cold War.  People around the world worried about nuclear war because of this conflict.  The Cold War completely shaped the world as it was happening.

Now that it has been over for some years, the Cold War is important mainly because it destroyed communism. Where there were once many communist countries, today only a very few can truly be called communist.  The Cold War helped to defeat communism.  By doing so, it changed the lives of huge numbers of people in the countries that were once communist.