The development of nuclear weapons had a very important aim: to act as a deterrent. Both sides feared at moments of key tension that the other side was about to launch a nuclear attack. This threat acted like a bargaining tool to intimidate the other side into cooperating.
This was demonstrated powerfully during the Cuban Missile Crisis when both sides believed the other was about to launch its nuclear weapon first. The idea of MAD (Mutually Assured Destruction) became central to the deterrent – the threat that if one side launched a nuclear weapon, the other side had enough time to do so too. The result would be that both would be wiped out and it would mark the end of civilisation.
Neither side crossed that line, even though it came very close. It was the policy of MAD which in the end probably prevented nuclear war from becoming a reality.