Wastegate control
This quite simply controls the flow of exhaust gasses and therefore the speed of the turbo and resultant boost pressure.
The speed at which the assembly spins is proportional to the pressure of the exhaust flow and the drag created by the compressed air and total mass of air flow being moved.
Since a turbo can spin to RPMs far beyond what is needed, or of what it is safely capable of, the speed must be controlled.

The problem in a turbo engine is that high intake pressures are prone to spontaniously ignite, a condition known as knock. So there is a theoretical limit on how much compression you make to the intake charge depending
A wastegate is a great way to slow up the turbo as the upper limits are reached. Aftermarket wastegates operate more quickly than standard ones and can be more finely tuned allowing large power gains.
The wastegate quite simply and cleanly diverts the exhaust gases away from the turbo thereby reducing the speed and amount of compression of intake charge.
Many modern cars will go into a limp home mode if the intake pressure is much higher. A full remap will override this and allow you to run with more boost. Some cars will require a higher capacity air flow sensor to cope with the extra boost readings it will be getting.