You need to be more precise in your question. But basically the US wanted to prevent Cuba from being communist in the domino theory that if one country is communist all the others around it will fall communist. Us tried to oust the leader in charge but they failed and it was a humuliation for the US and ot showed that we were trying to kill their leader which did not create good ties with the US to the Cuban. Missiles were pointed to the US and Russia put them there as part of the Cold war. They were allied with Cuba and we told them to take them down after three days. It was the closest to war but once again Cuba was a proxy conflict during the Cold War. Cuba has remained a communist place since then.
The doctrine that allowedpeopleliving in the territories to decide the issue of slaverythrough their governmentalbodies was called popular sovereignty.