Corridor of easily traversable terrain in the former West Germany
between the Rhine
river near Frankfurt
and the area of Erfurt and Eisenach.
If you were on the western border of the German Democratic Republic and you wanted to move, say, a few divisions of armor westward and into NATO-controlled western Europe, you would first have to reach and cross the Rhine river, and this would be the quickest and easiest way to do it. Not only does the Gap represent the shortest possible route from the East German border to the river, but it follows a fairly flat, well-developed (read: "paved") course and meets the Rhine at one of that river's narrower points. This is important, as if Warsaw Pact forces reached the Rhine, all bridges would of course be destroyed to halt the advance, and the river would have to be bridged or forded. The strategic importance of this corridor was known even before the partition of Germany, the Third U.S. Army following it eastward in the final stages of the European campaign of World War Two.
Given the importance of this area, it played a big part in both NATO and Warsaw Pact strategic thinking throughout the Cold War. Numerous studies and assessments were produced, and a significant amount of U.S. war games and training exercises (and presumably Soviet ones as well) simulated an attack along this corridor. It has been said that the primary purpose of the entire American military presence in Europe was stopping a Soviet attack at the Fulda Gap.
While a confrontation never arose, there was enough public speculation to sketch a rough outline of what would happen in the event of an attack through the Fulda Gap. First of all, the resultant battle would be waged mostly on the ground - enemy and allied forces would be too close together to utilize strategic bombing, (as this was prior to the Gulf War era of precision guided munitions) and enemy anti-aircraft capability would severely endanger low-flying craft. Dedicated anti-armor platforms such as attack helicopters and the A-10 would be expected to see significant use, however. Offensive forces would be primarily armor - the only thing strong enough to survive and fast enough to matter. An established infrastructure and many nearby caches of ammunition, fuel, spare parts, and other necessities would address the logistics and supply issues that have always plagued the use of armor in battle. Both heavy and light tanks would attempt to take ground, hold it, destroy each other, and just generally blow things up. There would, of course, be anti-armor forces as well, (to mention nothing of anti-anti-armor) comprised of a variety of elements, including infantry- and light vehicle-mounted anti-tank systems but most importantly artillery, especially self-propelled heavy artillery. All platforms, from infantry on up, could be expected to have and employ tactical nuclear weapons. Unless you were occupied with pressing matters such as killing the people in the other uniforms, you really wouldn't want to be there. When you get down to it, even if that was your job, you still wouldn't want to be there.
Regardless of the victor, exactly what would happen after an encounter at the Fulda Gap is somewhat unclear. Of course there is a good chance that Moscow and Washington would be glowing by this point, and if not a nuclear exchange, an attack through the Fulda Gap would almost certainly provoke a full-out, multi-front war, leaving many more theaters of war to consider. Obviously, this is a bit more academic now following German reunification and collapse of the USSR.
The term has also recently come to stand as shorthand for Cold War military attitudes, systems, and strategies unsuited for a modern situation. This refers to the fact that the Gulf War and subsequent small-scale, asymmetric confrontations in the '90s and early 2000s have provoked calls for a US military organized as a light, mobile, and flexible force able to quickly respond and deploy around the world, fighting minor national militaries and non-state groups. This stands in direct opposition to forces prepared for a Fulda Gap confrontation - heavy, static, anchored to a well-known battlefield, and prepared for a superpower confrontation. The cancellation of the Crusader gun system is an excellent example of an attempt to move away from a "Fulda Gap" Army.
The_Custodian has written several excellent nodes on the weapons, systems, and strategies associated with a possible Fulda Gap conflict, and I encourage you all to check them out.