A turbocharger (turbo) is used to speed up an engine through forced induction. It compresses the air and gases that go into the engine using a turbine which in turn increases the power of the engine. They are very useful and commonly used because they increase the power of the engine without having to increase the engine capacity. The downfall of a turbo is that they are set to kick in at a certain RPM (Rev Per Minute), so there is a lack of power up until you get to this set RPM, this is known as turbo lag.
Turbo's are most commonly used in diesels because even though they have a lot of torque they often lack power and can be very slow and sluggish, so a turbocharger is perfect for balancing this loss. You also find them being used in performance cars as they can make a quick car even quicker. In some cases you can have twin-turbo which obviously makes the forced induction even greater but the main use of the second turbo is to eliminate the turbo lag. The second turbo is a smaller one so that you can set it for the low revs and lead it on to the RPM that is set for the bigger turbo for the top end.
Turbochargers are fitted into a large range of production cars these days but there are many cases of people customising their cars to fit a turbo. There is normally a bit of fabrication work that is involved e.g. they may have to get a custom made inlet manifold to fit the turbocharger and the engine together. However, even though the turbochargers themselves are quite reliable because they are simply driven by the engines own exhaust gases, the internals of the engine may need to be changed to cope with the new power e.g. steel pistons and rods