Remapping is a method of changing the characteristics of the engine by electronically reprogramming the engines "brain" to make it more efficient and give extra power and torque.
An engine has several parameters that are controlled by this "brain" (or ECU as it is known) and these can be altered from the conservative original settings (that VW use) to higher settings. For example the fueling ratio's can be altered to give a more powerful combustion in the piston chamber. Similarly with turbo powered cars, the pressure in the system can be increased to give a higher combustion pressure and as a result more power. All in all tuners can alter in excess of 30 individual settings to free up more power in the engine. The better tuners tend to do more research and alter more parameters for a better balanced "map" and other tuners simply opt for upping the pressure and fuel mix.