Fail-Safe is a novel which above all is a product of its time, the early 1960's, when nuclear war between the U.S. and the Soviet Union was widely feared as imminent. In the story, a computer error causes a squadron of U.S. bombers to receive a (false) order to attack the Soviets with nuclear weapons. The "safeguards" built into the system that are supposed to prevent such an unauthorized attack then do the exact opposite, making it impossible to recall the bombers. The President, in order to demonstrate to the Soviet Premier that the attack is not intentional, must then order New York City to be destroyed by a nuclear bomb.
Though the plot may seem far-fetched from our present-day perspective, 55 years ago it expressed realistic fears about the potential for accidental destruction and a nuclear apocalypse. The Cuban Missile Crisis had just occurred in which the Soviets had nuclear missiles pointed at us "from 90 miles away." Automated systems and computers were a relatively new phenomenon and were not well understood by the public. Often, the assumption was that these systems could, and would, run amok and cause disastrous results.
Fail-Safe derived its power from these fears and possibilities. Though on the surface the message is that machinery and automation can get out of control, the underlying theme is that it is man and his own weaknesses that are the real danger. The failed attempts to recall the bombers, and the consequence that the President must order the bombing of one of our own cities, illustrate that because man has created this system and these weapons, sooner or later they are going to be used, intentionally or not.