It lets out pressure in the intake when you let off the throttle, it's a secondary form of letting out excess boost pressure to prevent "overcharging" your motor as you let off the throttle. The turbine still spins and your throttle plate is still closed, so it has to go somewhere.

Your wastegate lets out pressure from the exhaust end of the system. You need a BOV or have it recirculated back into your intake otherwise you'll damage the compressor housing or blow your motor.

And no, it doesn't really effect power because the turbine is still spinning (albeit at a lesser speed) when you go to shift into the next gear.