Both the U.S. and the USSR had the nuclear weapons to destroy the other side. This led to a situation in which neither side would dare to attack first, since the other would retaliate with equal or greater force. Nuclear weapons thus deterred both superpowers from attacking first. This policy was known as Mutually Assured Destruction (MAD). Khrushchev remembers:
I remember President Kennedy once stated (…) that the United States had the nuclear missile capacity to wipe out the Soviet Union two times over, while the Soviet Union had enough atomic weapons to wipe out the United States only once. (…) When journalists asked me to comment (…) I said jokingly, ‘Yes I know what Kennedy claims, and he’s quite right. But I’m not complaining. (…) We’re satisfied to be able to finish off the United States first time round. Once is quite enough. What good does it do to annihilate a country twice? We’re not a bloodthirsty people’.
Source: N.S. Khrushchev, Khrushchev remembers: the last testament (London 1974).