The United States entered the Vietnam War because it was concerned about the spread of communism. The Vietnamese insurgents were led by communists and therefore the US did not want them to come to power. It feared that a communist Vietnam would lead to a "domino effect" in which other countries of East Asia would become communist.
The US believed that this would be a danger to US allies in the area such as Japan, the Philippines, and Australia. It also believed that more communism anywhere in the world would be bad for the security of the United States. For this reason, it entered the war when the French left Vietnam and got more and more involved as it became clear the South Vietnamese army could not win on its own.