During the Cold War, the government in Cuba had been overthrow by Fidel Castro. Castro aligned himself with the Soviet Union and relied heavily on their support. The United States government, be wary of the possible treat to their south conducted multiple spying operations.
On October 14, 1962, an American U-2 spy plane photographed pictures of a Soviet nuclear missile being assembled in Cuba. The United States, upon receiving this information, began to get very nervous. This was because the nuclear missiles were within 90 miles of Florida.
The Soviets decided to send missiles to level the playing field. Up until that point, the United States had nuclear missiles set up in Western Europe, all pointed at the Soviet Union.
The United States set up a blockade around Cuba to stop the shipment of nuclear missiles. The blockade was a success. On October 27th, an American reconnaissance plane was shot down over Cuba. The United States began to prepare an invasion force in Florida.
Throughout this time, the two countries had been talking to each other in order to advert a nuclear war. On October 26th, Soviet Leader, Nikita Khrushchev sent a proposal in which the Soviet Union would remove it's weapons from Cuba if the United States agreed not to invade Cuba. Kennedy agreed to also remove the United States' weapons from Turkey.