What you are asking about here was a central idea of the Cold War. This is the idea of the "domino theory." This was the idea that if a country (in this case Vietnam) became communist, then other countries near it would become communist. This would be the start of a chain reaction in which countries all over the world became communist.
Have you ever seen when someone sets up a line of dominos and then knocks one over and it makes the whole line fall down? This is what this theory is named after. The theory said that Vietnam would be like that first domino. If it fell (became communist) it would hit the next domino (country) and that country would become communist.
This theory was used to explain why it was important for the US to go to war in a country that seemingly had very little to do with the national security of the US.
America was paranoid about the communist take over in South East Asia. President Eisenhower came up with the domino theory which was
you have a row of dominos set up, you knock over the first one and what will happen to the last one is a certainty, that it will go over very quickly.
Which meant that if one country fell into the communist sphere of influence the rest would follow like a row of dominos (falling)
What Eisenhower was trying to say that if they allowed communist takeover in Vietnam it would lead to the takeover of Laos, Comodia, Thailand, Burma and maybe India.
Which sums up the entire south east Asia. south east Asia was very important to the US for its military and trade.
hope this helped.