What was the problem that the US faced in Cuba in 1962 and how did it end?

The problem became known as the Cuban Missile Crisis. It was the point during the "Cold War" when the USA and USSR became perilously close to actual nuclear warfare.

Reconnaisance photographs taken by a high-altitude U-2 spy plane showed that the Soviet Union had armed Cuba with nuclear Medium Range Offensive Ballistic Missiles.

President Kennedy placed a naval quarantine around Cuba to stop further weapons being taken to the island, and Kruschev stepped down and removed the missiles after the US promised not to attack Cuba.