The domino theory refers to any chain of events set off by a single event.
One country falls to a foreign influence, in turn the country next to it falls, and then that one causes another country to fall etc. until all the countries in the area have fallen. The example contribute above is the classic given for the Domino Theory.
During the Cold War, the Soviet Union used the Domino Theory to get all the countries in Europe to be communist, and they were successful because no one would decline them because they were a world super power and they knew they would be attacked if they did decline.
John F. Kennedy was elected president of the United States in November, 1960. In the first speech he made to the American public as president, he argued that if South Vietnam became a communist state, the whole of the non-communist world would be at risk. If South Vietnam fell, Laos, Cambodia, Burma, Philippines, New Zealand and Australia would follow. If communism was not halted in Vietnam it would gradually spread throughout the world.
America's involvement in Vietnam ended in 1973. The war had cost one billion dollars a day at its peak, dropped 7 million tons of bombs(more than the entire total of all participants in World War Two). The cost of the war in 1968 alone was $88,000 million while the combined spending on education, health and housing in that year was $24,000 million.