Dump valves are fitted to the engines of turbo charged cars and sit between the turbo outlet and the throttle body. When transitioning from a boosted state to a closed throttle state (as in between shifts), due to inertia, the turbo continues to pressurize air, but the closed throttle prevents the compressed air from entering the engine. In this case the pressure exceeds the preset spring pressure in the dump valve and the excess pressure is bled off to atmosphere. 
The dump valve is the black plastic saucepan shaped object that you will see connected between the intercooler and the air inlet hose to the turbocharger. You will also see a small hose leading from the top of the valve to the inlet plenum on the engine. Inside the valve are a rubber diaphragm and a steel spring, with a small insert to support the diaphragm where it seats against the dump valve body. The dump valve has basically two operating conditions; throttle open, and throttle closed. When the throttle is open, the boost pressure coming into the valve from below the diaphragm is equaled by the pressure onto the top of the diaphragm that comes via the small hose from the engine plenum chamber. As the pressures are equal, the spring holds the diaphragm onto its seat, and prevents the pressure venting away. When the throttle is closed, the pressure coming into the top of the valve is significantly reduced, (often to a vacuum), and the pressure below the diaphragm lifts it away from its seat, allowing the excess pressure to vent away. As the throttle is reopened, the pressures again equalize, the spring pushes the diaphragm onto its seat, and the boost pressure cannot vent away.
There are a number of reasons for manufacturers to fit a dump valve. Without a dump valve, when the throttle was closed, the build up of boost pressure would be immense, very similar to closing a quickly flowing water tap. This excess of pressure, (which could be over five times the running boost pressure), would put the components of the system under a great strain. It would try to burst the intercooler and pipe work. More significantly, it would put a large strain on the turbocharger itself, firstly stalling the compressor shaft, then trying to force the compressor wheel out of the turbo, against its bearings. So, the dump valve prevents mechanical damage to the intercooler & turbo pipe work, prolongs turbocharger life, and prevents excessive turbo - lag that would be caused by the compressor shaft stalling. 
For convenience of plumbing, many manufacturers fit the dump valve as close as possible to the air filter. This also means that it is connected to the hot side of the intercooler. The compressed air from the turbocharger can reach temperatures in excess of 150°C, and this will drastically shorten the life of the rubber diaphragm. Also, for better response, it is preferable to situate the dump valve near to the throttle plate of the engine. If you look at the standard pipe work of an RS 500, you will see that Ford Engineers re-sited the dump valve on this homologation model.
To enable the re-positioning of the Dump Valve, some manufacturers produce complete kits consisting of a Dump Valve, a fabricated aluminium pipe to go from the intercooler to throttle body, and all of the relevant silicon hoses and clips to carry out the conversion. The kit also includes two polished aluminium blanking plugs to fit in place of the original dump valve.
Dump valve is very stable. The only thing that can go wrong with a dump valve is that the diaphragm can become holed. If this happens, it will not seal, and the boost pressure leaks away all of the time. This will cause the turbocharger to work harder to overcome the leak, (turbochargers will work as hard as they have to, to give the required boost), and this will be noticeable to the driver, as a lack of boost response.