Via Wired, the U.S.S.R. built a fail-safe device à la Dr. Strangelove—not to deter us, but to deter themselves:
The point of the system...was to guarantee an automatic Soviet response to an American nuclear strike. Even if the US crippled the USSR with a surprise attack, the Soviets could still hit back. It wouldn't matter if the US blew up the Kremlin, took out the defense ministry, severed the communications network, and killed everyone with stars on their shoulders. Ground-based sensors would detect that a devastating blow had been struck and a counterattack would be launched.
By guaranteeing that Moscow could hit back, Perimeter was actually designed to keep an overeager Soviet military or civilian leader from launching prematurely during a crisis. The point...was "to cool down all these hotheads and extremists. No matter what was going to happen, there still would be revenge. Those who attack us will be punished."
Given the paranoia of the era, it is not unimaginable that a malfunctioning radar, a flock of geese that looked like an incoming warhead, or a misinterpreted American war exercise could have triggered a catastrophe. Indeed, all these events actually occurred at some point. If they had happened at the same time, Armageddon might have ensued.
Perimeter solved that problem. If Soviet radar picked up an ominous but ambiguous signal, the leaders could turn on Perimeter and wait. If it turned out to be geese, they could relax and Perimeter would stand down. Confirming actual detonations on Soviet soil is far easier than confirming distant launches.
As long as no one rides an H-Bomb down like a bronco...