How did the buildup of nuclear weapons promote peace during the cold war?

The development of nuclear weapons was a decisive factor that generated stability, erroneously called peace, during the Cold War.

This was because in both ideological sides of this confrontation, both the leading powers (United States and the Soviet Union respectively) and their allies or secondary powers (Great Britain, France, China, among others) developed nuclear weapons capable of literally destroy much of civilization. Therefore, taking into account this situation, neither of the two blocks was willing to a large-scale nuclear confrontation, so they preferred to carry covert wars through more isolated countries (Vietnam, for example), for fear of destruction total through a nuclear war.

This meant that certain parameters of stability were maintained during the Cold War, although it was not a total peace.