To be honest..... most people who fit them probably don't know what they do either and only fit them for the sound!
The idea behind them is pretty simple though, A turbo is simply a compressor that compresses the air going into the engine, while on full throttle and high revs the turbo will be spinning at very high speed and pushing a lot of air into the engine, which is fine while the throttle is open. but as soon as the throttle is closed (i.e. when changing gear) the turbo is still spinning at full speed but there is now nowhere for that air to go, so it will increase the air pressure behind the turbo until it gets so high the turbo can't compress the air any more and it will "stall" the turbo and slow it down.
Slowing the turbo down during a gear shift is bad because it then takes time for it to spin back up to speed and deliver full power again. all a dump valve does is release the excess pressure once it exceeds a certain level (that's the noise you hear) and therefore keeps the turbo spinning faster during gear changes which mean less time is taken to get full power back after a gear change.
The really silly ones are the people who fit a fake dump valve, which is basically a speaker that makes the noise at the correct time but does burger all else!