Nuclear missiles.
The Soviets placed nuclear missiles in Cuba. They had to be removed. We moved military forces towards Cuba with the intent to destroy them. The Soviets removed them
They placed a naval blockade around Cuba.
The Cuba's alliances with the soviets worried Americans for a for different reasons. They thought that the fight between them would turn into a cold war.
The Soviets could easily land an attack on the United States from Cuba.
The Soviets (Russians) removed their missiles from Cuba.
The Soviets withdrew their missiles from Cuba at the threat of war.
It started with the Soviets setting up launch bases, in Cuba, that could hold Inter-Mediate Ballistic Missiles (IRBM). After a lot of laws and failed missions, the Soviets decided that they will remove the missiles from Cuba, if the US would remove the missiles from Turkey, and around Europe.
Castro was dictator of Cuba, which was the closest Soviet-bloc nation to the United States. Because of his country's location, the Soviets stationed a small motorized rifle division called the Soviet Brigade in Cuba (a brigade was not a common formation in the Soviet Army; what the US calls brigades the Soviets called regiments) in Cuba and put a lot of money into Cuba to help disguise the fact that Cuba's economy was terrible.
Soviets build nuclear missile sites in Cuba.
John Kennedy ordered this blockade to stop the Soviets from delivering missiles to Cuba. The incident is known as the Cubam missile crisis.
The U.S. agreed to not invade Cuba. They also agreed the removal of U.S. missiles in Turkey in return the Soviets took the missiles from Cuba.
The Soviets already knew that the US had nuclear missiles in Turkey, placing nuclear missiles in Cuba would simply achieve nuclear parity. Also following the failed Bay of Pigs invasion the leader of Cuba Fidel Castro wanted assurance from the Soviets of their security against future invasion, the Soviets believed that nuclear missiles would provide this security at the least cost.