From Wikipedia
Two-speed and two-stage superchargers[edit]
In the 1930s, two-speed drives were developed for superchargers. These provided more flexibility for the operation of the aircraft, although they also entailed more complexity of manufacturing and maintenance. The gears connected the supercharger to the engine using a system of hydraulic clutches, which were initially manually engaged or disengaged by the pilot with a control in the cockpit. At low altitudes, the low-speed gear would be used in order to keep the manifold temperatures low. At around 12,000 feet (3,700 m), when the throttle was full forward and the manifold pressure started to drop off, the pilot would retard the throttle and switch to the higher gear, then readjust the throttle to the desired manifold pressure. Later installations automated the gear change according to atmospheric pressure.
Another enhancement was the use of two compressors (also known as stages) in series, such two-stage superchargers were also always two-speed. After the air was compressed in the low-pressure stage, the air flowed through an intercooler radiator where it was cooled before being compressed again by the high-pressure stage and then possibly also aftercooled in another heat exchanger. Two stage compressors provided much improved high altitude performance, as typified by the Rolls-Royce Merlin powered Supermarine Spitfire Mk IX and the North American Mustang. In some two-stage systems, damper doors would be opened or closed by the pilot in order to bypass one stage as needed. Some systems had a cockpit control for opening or closing a damper to the intercooler/aftercooler, providing another way to control temperature. Rolls-Royce Merlin engines had fully automated boost control and all the pilot had to do was advance the throttle, the control system would limit boost as necessary until maximum altitude was reached.
If I am correct to the two speed part is literally the same concept as gears in a car. One speed makes the supercharger spin slower, one faster. The two stage part allows for compressing the air twice, or possibly once if desired. The effect of this is a finer control as opposed to just "slow and fast" So that an engine can receive closer to maximum boost without going over the limit at a wider variety of altitudes. At least I think that is how it works.
