Why was Cuba an important place in the Cold War?
Following a revolution in 1959 Cuba adopted Communism, being the only state in the Americas to have a do so, or at least to have a Communist government that lasted. (In fact, it's still in office in 2006). An attempted invasion from the US ('Bay of Pigs' [and no it was not a bay full of floating pigs :^P]) was a fiasco and in 1962 Khrushchev tried to station long-range missiles on the island. This attempt led to the 'Cuban missile crisis' of 1962.
When this began, the U.S. sent Fidel Castro a letter stating that the U.S. will remove their missiles from Turkey if Cuba remove theirs. Castro agreed to this and did so, marking an end to the Cuban Missile Crisis.