There were several factors that lead to the Cuban Missile Crisis of 1962, including:
A) The United States putting missiles in Turkey. This country is located close to the Soviet Union and their satellite nations during the Cold War era.
B) The Soviet Union putting missiles in Cuba. Cuba is only 90 miles from the US, putting them in close proximity to a Soviet attack.
This crisis lasted 13 days in October of 1962, and was resolved when Kennedy and Khrushchev came to an agreement. The US would pull their missiles out of Turkey and promised to never invade Cuba again. The Soviet Union would pull their missiles out of Cuba under the supervision of the United Nations.