As noted in Airplane Aerodynamics by Dommasch, Sherby, and Connolly, 1967, Pitman Publishing Corporation, New York...
It is a relatively simple matter to fit to an engine a large supercharger that is capable of providing excessive MAP (manifold absolute pressure) at full throttle at sea level. Ascent to altitude permits opening the throttle to compensate for reduction in air density without exceeding the rated MAP. In fact, if MAP is kept constant by gradually opening the throttle as altitude is gained, the reduction in exhaust back pressure will cause an increase in airflow that actually increases engine power. The altitude at which the throttle must be fully opened to maintain a given MAP at a given RPM is known as the critical altitude of the engine for the given RPM-MAP condition. Above this altitude the mass air flow, and consequently the power output, diminishes because of the reduction in air density. A gear shift providing a higher speed for the supercharger impeller, or an auxiliary stage of supercharging, simply extends the above conditions to a higher altitude.
This explanation is given and detailed on page 251 and pages following in the source given above.