The domino theory, a dominant theory within US political state narratives from the 1950s to the 1980s, stated that if one country became a communist state, other nations surrounding that area would be more likely to become communist and would fall under communism one after another, like a stack of dominoes. As such, the United States developed a policy of containment, in which the United States would not fight against an established communist country but would fight the spread of communism to surrounding areas. Of course, the United States's interest in containing communism was not one of ensuring/advancing human rights (consider the ongoing massive human rights violations of the United States against its black citizens that were happening during that time period). Rather, the United States was concerned with maintaining its position as a dominant economic and military power around the world, and communism was politically and economically in contradiction with the United States's economic and political interests in being a dominant world power based in capitalism and militarism.

The domino theory was a crucial factor in America's military involvement in Vietnam. Among policy-makers in Washington, it was widely believed that if one country fell to communism, this would inevitably lead to others following suit. This was by no means an ungrounded fear: as an internationalist ideology, communism was well placed to transcend national boundaries and spread throughout the globe, especially in the developing world, where states were on the whole much weaker than in the West.

Vietnam occupied what was for the United States a strategically important position in East Asia. The United States had military bases in Japan, South Korea, and the Philippines, and so the last thing anyone in the Johnson Administration wanted was to see a new communist government established in what it regarded as a US sphere of interest. If the North Vietnamese, in concert with the South Vietnamese communist guerrillas of the Viet Cong, prevailed in the civil war, it was genuinely feared that other states in the vicinity would soon fall under communist control as they were deemed neither strong nor stable enough to withstand a full-blown insurrection. This led to the felt necessity for significant American involvement in Vietnam, both diplomatically and militarily.

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.