We can look at the significance of this event in two ways.
Internationally, the revolution was significant because it put a communist country close to the coast of Florida. During the Cold War, this was very significant because it could be seen as an example of the spread of communism. This allowed the Bay of Pigs and the Cuban Missile Crisis to occur.
For Cuba, this was also significant. It overthrew a dictatorship that was brutal and which was run for the benefit of a few elites. However, it also brought on a communist dictatorship that could be brutal and which has run their economy into the ground. In this way, it was significant for Cuba as well as for the world as a whole.
The Cuban Revolution was a big event. The United States had been working to prevent the spread of communism since the end of World War II. In many instances, we were successful in preventing its spread. However, when Cuba became communist, things changed for the United States. It was one thing to fight the spread of communism in Europe or Asia. However, when Cuba, only 90 miles from Florida, became communist, it brought the communist threat right to our doorstep.
The arrival of communism heightened tensions between the United States and Cuba. We tried to overthrow the communist regime with the Bay of Pigs invasion. This invasion was a disaster, causing tensions to deteriorate further. In 1962, the Soviet Union put missiles in Cuba, leading to the Cuban Missile Crisis. The world worried about a nuclear confrontation after we blockaded the Cuban coast. Fortunately, that crisis ended peacefully. The United States and Cuba have had a very cold, almost nonexistent, relationship since Cuba became communist. Only very recently has that icy relationship thawed somewhat.
The people of Cuba hoped their revolution would improve their lives. In many ways, however, conditions for the average Cuban are very similar to what they experienced before the Cuban Revolution began. Many people remain poor and basic freedoms, such as freedom of speech, don’t exist.