Mutually Assured Destruction (MAD) is a military doctrine which relies on the principle that if a country with nuclear capabilities attacks another nation with nuclear weapons, the end result will be nuclear annihilation for both nations. Since this outcome is not desirable, the theory goes that by stockpiling nuclear weapons, a nation will protect itself from nuclear attacks, since no nation would want to risk annihilation. This doctrine was never officially adopted, but it led to an arms race between many major nations.
This concept relies on a principle of game theory known as the Nash Equilibrium. The idea is that because all parties involved know what everyone else is capable of, there's no reason to change strategy or to make sudden policy decisions. In fact, in a Nash Equilibrium, stepping outside the equilibrium can totally upset the balance, leading to a negative outcome in which no one wins. In other words, Mutually Assured Destruction is a zero sum game.
There are several problems with the concept of MAD. The first, from a foreign policy perspective, is that it tends to discourage summits, meetings, and treaties. The parties involved have no reason to meet to discuss and resolve issues, and in fact they tend to prefer remaining aloof. This is not very productive for resolving long-term conflict.
Another issue is that Mutually Assured Destruction encourages infinite increases to a nation's stockpile of nuclear weapons. Think about it this way. If you have a war with your neighbor and your neighbor has a stick, you are going to acquire a stick too. But you might wonder if your neighbor has an ax, in which case you buy an ax, your neighbor sees the ax and buys a gun, you see the gun and buy a cannon, and so forth. Nations which subscribed to this doctrine were constantly forced to upgrade weapons systems, test weapons, and accrue ever-growing stocks of weapons to indicate that they were prepared for a nuclear war.
As the Cold War wound down in the 1980s, many nations realized that MAD was a foolish and potentially very dangerous doctrine. In response, nations like the United States and the Soviet Union started meeting to discuss the arms race and to reach a resolution which would allow both nations to destroy excess nuclear weapons stockpiles and focus on cooperation instead of an endless standoff.
By the time Mutually Assured Destruction had been largely abandoned, it had entered the popular consciousness. The idea of a nuclear winter created through nuclear aggression is a theme in many apocalyptic novels, films, and television shows, and the specter of Mutually Assured Destruction hovers in the minds of some foreign policy students as well, especially with more and more countries developing nuclear capability.