Power is produced when a mixture of air and fuel is burned inside an engine cylinder. If more air is forced into the cylinder, then more fuel can be burned and more power produced with each stroke.
A supercharger compresses the air intake to above atmospheric pressure which increases the inlet air density to the engine.
Naturally-aspirated engines operate with uncompressed air at atmospheric pressure, 14.7 pounds per square inch, or 1 Bar. When the cylinder intake valve opens, atmospheric pressure pushes air into the cylinder as the piston is lowered. When the exhaust valve opens, the piston pushes the exhaust gases out into the exhaust system, again at normal atmospheric pressure. Since both the intake and exhaust ends of the system are at the same air pressure, there is no natural flow of air through the system. In such engines, valve timing, camshaft timing & exhaust sizing are critical to getting the maximum power output.
In a supercharged system, there is a greater air mass flowrate, that is, a higher density and speed of air flow. Air pressure is increased by the compressor on the way in to the engine, more power is produced by combustion, and the exhaust gases exit much more rapidly, making the timings and exhaust sizing less important. Although some of the extra power produced must be used to drive the supercharger, the net result is more total power from the system. The supercharger includes a bypass valve system which allows the supercharger to 'idle' when 'high power' is not required, turning off the pressure and allowing the engine to run as a naturally aspirated engine. The bypass valve can be mounted remotely, or directly onto the intake port.
A turbocharger is a forced induction system that uses wasted kinetic energy from the exhaust gases to increase the intake pressure. Like superchargers, turbochargers increase the amount of air that flows into the engine, but they have a negative effect on the flow of air out of the engine.
This means that for maximum power output, valves, cam timing, and exhaust system design are more important in turbocharged systems than in supercharged systems.