Best description I've seen is from Wikipedia.
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.
Even with a dump valve the compressed air acts as a brake on the turbo (slowing it down), because the pressure on the backside of the turbo is at a higher pressure than on the front side (and the air actually wants to flow through the turbo backwards).
A blowoff valve is a more elegant solution to this problem by allowing the turbo to "freewheel" when the throttle is closed (equalizing the pressure on both sides of the turbo). Unlike a dump valve a blowoff valve can be used at multiple boost settings without reconfiguration.
Blowoff valves are sometimes incorrectly called dump valves because they serve a similar function, but they are very different solutions to the same problem.
More here
http://en.wikipedia.org/wiki/Dump_valve
http://en.wikipedia.org/wiki/Blow_off_valve