Turbo & supercharger both are forced induction systems . They compress air flowing in engine. Compressed air means more air in cylinder . More air in cylinder means more fuel sucked In . Large amount of air & fuel make boost explosion in cylinder produces more power . Turbo/supercharger engine generate more power overall than without turbo/supercharger engine.
Turbocharger or supercharger engine suck 50 percent more air into cylinders. You would expect to get 50-percent more power But It's not perfectly efficient, though, so you might get a 30% to 40% improvement instead.
The main diffrence between Turbocharger & supercharger is power supply . Turbocharger runs on waste gases exhausted after combustion. After combustion engine leaves exhaust gases which turn spins the compressor. On other hand supercharger gets power from belt drive which is directly connected to engine . Belt drives the supercharger compressor & compressor start compressing air then deliver to engine.
Turbochargers are more efficent because it uses 'waste' energy as a power source. Supercharger are easy to install but more expensive