Supercharging your car makes more power by forcing more air into your engine just like an Exhaust driven Turbocharger does.
This allows you to burn more fuel.
The difference is that the compressor is driven directly by the engine rather than the exhaust gasses. The one shown is a VW VR6 Motor with an aftermarket low boost "supercharger" fitted.
In this case it is actually a centrifugal compressor just like a Turbocharger uses, but driven by an auxiliary drive belt.
Most superchargers are "screw" types, and positive displacement like the one on the left.
The VR6 one at the top of the page is unusual in that it uses a turbocharger type centrifugal compressor instead.
The Supercharger has a few disadvantages over a turbocharger, in that it takes power to drive the compressor directly from the engine. This is then lost or wasted. A turbocharger on the other hand uses waste exhaust gasses to drive the compressor so is more efficient.
But the supercharger has advantages too! There is no lag! Boost is always available, no matter what. With a turbocharger you have to wait until the engine starts to produce enough exhaust gas to spin up the turbo to give you some boost.
For ultimate BHP, like a top fuel dragster with 5000bhp supercharging is the only option! They accelerate from zero to 300 MPH in 4 seconds. A turbo would still be winding up!