The answer is containment.
The foreign policy of containment called on America to stop the spread of communism all over the world. The reason why the American government wanted to do this was because they feared if one country fell to communism then neighboring countries would also fall to communism. This concept is known as the Domino theory (or domino effect).
Since North Korea was communist and trying to spread their influence into the capitalist South Korea, America made sure to intervene. Their goal was to make sure that communism did not completely take over South Korea. Ultimately, the Korean War ends in a stalemate, with North Korea still being communist and South Korea still being capitalist.
