The Vietnam war matters at the begin because, China had become communist in 1949 and communists were in control of North Vietnam. The USA was afraid that communism would spread to South Vietnam and then the rest of Asia. It decided to send money, supplies and military advisers to help the South Vietnamese Government.
The Vietnam war maters today because, the policy of containment led the United States into a wide array of conflicts ranging from Korea to Vietnam, and whose legacy is still with us in the economic embargo of Cuba and a destabilized Afghanistan.
The severed snake represents the colonies if they do not work together. He used this to explain to colonists that the only way to defeat the British was to stand together with everyone together like the parts of the snake.