This expedition is known as the Bay of Pigs invasion. This operation took place in 1961, and its main purpose was to remove Castro from power and lead a counterrevolution directed by the CIA. The United States wanted to invade Cuba in order to take over its government and manipulate it to the advantage of the United States.
However, this operation was a complete failure. After the troops landed in Playa Giron, the American army was overwhelmed by local militia, which was personlaly directed by Castro. Moreover, the invasion solidified the popularity of Castro as a national hero, while pushing Cuba closer to the Soviet Union.