When you take your foot off the gasspedal the throttle plate is shut/closed. The turbo is still spinning (as long as the engine is running) and blowing air through the IC and agains the closed throttlebody. All that boost/airpressure has nowhere to go, it's trapped between the throttle plate and the compressor. This is where the DV comes inhandy, the divert valve/dump valve opens up (when the pressure exceeds the set DV pressure) and eihter diverts the airpressure back into the TIP or dumps it info the atmosphere. If the DV has a to stong spring (airpressure relase set to high) or the DV dont work/open you will get whats called compressor surge (distressing sound). It can easily turn ugly, with shattered wheels or shaft bits all over the place. The dump valve prevents this condition, because as soon as the throttle is shut, it vents the excess pressure from the pipes, preventing this surge. This will reduce wear on the turbocharger and engine
Divert valve (DV) vs. dump valves (Blowoff) :
On engines with MAF (mass airflow sensor) its NOT recomended to use blowoff dump valves. When the blowoff valve dumps the compressed air into the free-atomsphere the MAF/ECU don't registed this (it still thinks the air is in the system). This results in a fuel-rich mixture after each valve actuation becuase the atmospherically vented air is not subtracted from the intake charge measurements. Therfore use divert valves!
Throttle response:
The MODIFIED dv placement (closest possible til the throttle boddy) is regarded best. The pressure build up starts at the throttle plate, this is where you want to divert/dump the 'over-pressure'. Therefore its most logical to place the DV on the cold side of your IC.
Stock:
As this illustration shows, the stock placement of the DV dumps hot air back into the turbo inlet pipe (TIP).

Modified
If the DV is re-located as this illustration shows, the DV dumps the cooled air back into the TIP.
Cooler air has a greater density. The greater the density of the charge mix in the cylinder the more power generated on combustion.

Blowoff Dump Valve:

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