The name of the leader that you are asking about is Fidel Castro. He was the communist leader of Cuba from 1959 until he retired, turning over power to his brother Raul Castro, in 2011.
Fidel Castro was a rebel leader in Cuba beginning in the early 1950s. In 1953, he and a group of followers attacked an army barracks but were badly defeated. Castro fled to Mexico. In 1956, he returned and started another rebellion. This one was more successful. The rebellion was against Fulgencio Batista, who was an authoritarian dictator and widely hated in Cuba. The rebellion was successful, and Batista fled the country on New Year’s Day, 1959.
The US tried to overthrow Castro when it became clear that he was more inclined to make a deal with the Soviet communists than with the United States. The US did not like the idea of a communist country so close to its own shores. The most notable episode in which they tried to overthrow him was the invasion (by Cuban exiles backed by the US) at the Bay of Pigs in 1961.
Anybody in America who was alive during those days will always remember the terrible black cloud of fear that hung over the world during those days. The Soviets wanted to install short-range atomic missiles in Cuba, only about sixty miles from the U.S. Our government threatened to sink the ship carrying the missiles and headed straight for the Caribbean. The Soviets said that would be an act of war. Both sides were loaded with enough atomic bombs to blow up the entire world. We went to bed not knowing whether we would wake up in the morning. This was the first time the U.S. had been so seriously threatened with heavy bombardment. We had been protected by the Pacific Ocean on one side and the Atlantic Ocean on the other. All of a sudden every American was under the gun, just like the people of England during the Blitz, and like the peoples of so many other foreign countries. The Cuban news was in the newspapers, on the radio, and on television every minute of every hour. Our country had several advantages if an atomic war broke out. We were ahead of the Soviets in the nuclear development, and we had short-range missiles pointed at them from many locations. We also had access by planes, submarines, and surface warships. They were trying to change the balance--and they would have done so if President Kennedy hadn't shown great poise and leadership. When the Soviet ship with the atomic warheads turned back at the last moment, it was a conspicuous turning point in the Cold War. We all felt that things would have to improve after that critical moment in history. I must say that the American civilians acted courageously. But I guess they had no other choice. Cuba has suffered from an American embargo for many years because of Castro's collaboration with a country that could have killed millions of Americans with atomic missiles. The missiles had multiple warheads. One missile could carry a number of bombs which could explode in various places.