A UFO is detected on early warning radar systems, putting air command on high alert.
As the UFO is identified, a computer short in the air command computer system sends an erroneous "go" code to Bomber Group 6 who then departs with the mission of dropping nuclear weapons on Moscow.
The on board Fail Safe system authenticates the erroneous go code as genuine. The system cannot differentiate between a and a real command, or an incorrect, but valid command.
Radio jamming prevents communication with the bombers until they have past their recall point, and are trained to ignore all voice commands.
The rest of the film focuses on the human-computer interaction, more specifically how the US deals with the aftermath of the computer glitch. They communicate with the Soviets using the Moscow-Washington hotline in an attempt to mitigate the fallout and avoid a large scale nuclear war due to the computer short.