The domino theory was extremely significant as a reason for the United States to get involved in the conflict in Vietnam. The domino theory was really just a way of justifying the theory of containment, which was the dominant factor in US foreign policy for much of the Cold War.
During the Cold War, the US was dedicated to preventing the spread of communism. This was the idea of containment. The US did not try to roll back communism where it already existed. Instead, it simply said that it would resist any expansion of communism to places where communism did not already exist. The domino theory was a way of justifying the idea of containment. The domino theory held that, if one country fell to communism, it would cause other neighboring countries to fall as well, just as the fall of one domino can topple a line of dominos set up for that purpose.
The US got involved in Vietnam because of these fears. It feared that a communist takeover of Vietnam would mean that communists would then take over all the other countries of Southeast Asia and might come to threaten US allies such as the Philippines or even Japan. Without the domino theory, Vietnam would have been an unimportant (to the US) country far away from the US and unable to hurt the US. With the domino theory, it became a threat to US security. Thus, the domino theory was an extremely significant reason for the US to get involved in Vietnam.