The main purpose of Turbocharger is to bring back part of the energy of exhaust gases to the cycle.This is done by feeding the ambient air at pressure with a small compressor which is driven by a small turbine which gets power from the exhaust gases.This increases the volumetric efficiency of the engine more than one.
Because of this features in higher power and thus higher speed of the driven vehicle.
A turbocharger is two turbines in one. There is an exhaust turbine and and intake turbine. The exhaust comes out of the engine with high velocity and with some pressure as well. This exhaust gases are then diverted into the exhaust turbine which extracts the energy from the exhausts momentum. This energy (rotating turbine) is then transfered via shaft into the intake turbine. This turbine is designed to take the energy from the rotating shaft and create positive pressure into the engine's intake manifold. Usually, an engine creates a vaccuum which draws air into the cylinders. In the case of a turbo, the air is forced in by the added pressure. As such, the engine can intake more air. With the addition of air comes the ability to burn more fuel. More fuel = more power.