A Cuban nationalist named Fidel Castro rose to power and began turning Cuba into a communist country. Cuba formed an alliance with the Soviet Union prompting America to plan an invasion to get Castro out of power.
The invasion was planned during Eisenhower's presidency but wasn't put into effect until March of 1961, after Kennedy was inaugurated. It was at this point that the U.S. CIA joined forces with the Escambray rebellion, a group of Cuban insurgents who opposed Castro and sought to regain political power. After training about 1,500 Cuban men, America was ready for the invasion.
The invasion finally began on April 17, 1961. However, Fidel Castro gained knowledge of the invasion beforehand and his troops were prepared for battle. This resulted in the CIA and Cuban citizens losing terribly to Castro's men. The Cubans fighting against Castro were captured and held as prisoners for a year and a half. The Bay of Pigs Invasion was a failure.