The impact was one based on strategic location. NATO had long had nuclear missiles in Turkey, not far from the USSR. Due to the limited range of Soviet missiles of the day, the USSR felt it needed a capacity to strike the U.S. heartland. The need was based more on the desire to contain global U.S. power, and less on the desire to simply slaughter the Americans. Fidel Castro's Cuba provided the perfect location for the Soviets to place firepower close enough to the U.S. to provide a counterbalance to American firepower in Europe. U.S. desires to remove Castro made him very nervous of the Americans, so his alliance with the Soviets was an easy one.
So to answer your question, the Cuban Missile Crisis was really about the location of strategic weapons and the desire of both the Americans and Soviets to contain each others power in the world. The American advantage in weaponry led to the Soviet need to counter it. Strategic weapons in Cuba, it seemed at the time, was the best way to counter that American advantage.
However, both the Soviets and Castro miscalculated, as they did not believe the U.S. was willing to go to war over the issue. Whether or not JFK planned to go to war or not was irrelevant, because the Soviets thought he would. While the Soviets wanted a strategic launching pad in Cuba, they were not willing to start World War III over it.
This is a very complex issue, so hopefully this helps a little.
