A turbocharger basically is two turbines in separate housings that are mechanically connected. As exhaust gas exits the manifold, it hits the turbocharger, specifically, it enters the exhaust turbine housing. When it does, the gas spins the turbine. Because the turbine is connected to another turbine by a rod, another turbine spins. This second turbine has an inlet and an outlet. The inlet connects to ducting that goes to the MAF sensor, then filter. The outlet on the high pressure turbos goes to an intercooler, then to the throttle body, and etc.

Basically, it's a form of forced induction, rather than natural aspiration. A running engine naturally creates a vaccuum on the intake side, that increases as rpm and load increases. And because the output the engine produces is directly related to the amount of air and fuel it can consume, a turbo charger can increase power output.