Why is The Persian Gulf War so important to the United States?

2 answers

Any war is important to those who fight in it and their families.

As for foreign policy, hang on and I will find a wiki party line.
Here is a reasonable summary from PBS:
http://www.pbs.org/wgbh/americanexperience/features/general-article/bush-gulf-war/

Note that this was an international coalition, including states that had been enemies in the Cold War, agreeing that the invasion of Kuwait by Iraq must be reversed.