Turbos are a form of supercharger; they add pressure to the inlet side of a combustion engine. Because the air going into the engine is therefore at a higher pressure than normal it is more dense and so carries more oxygen, if you carry more oxygen you can burn more fuel, if you can burn more fuel you can release more energy, this added with more efficient fuelling will give more power from each combustion in the cylinders.
So how does a turbo work? Very simply the exhaust gas flow of the engine is used to spin a turbine which is connected by a drive shaft to another turbine which compresses the air going into the inlet side of the engine. Therefore the higher the revs the more 'boost' is available via the turbo. Alongside the fact that a turbo needs time to 'spin up' (turbo lag) this is why a turbine tends to 'kick in' at a certain revs or over a certain rev range. The first production turbos tended to be an on or off affair and would sometimes catch out the unwary driver and throw the car into the scenery.

Technology moves on though and great efforts have been made to smooth out the kick that is inherent when a turbo spins up and adds the boost.

The first passenger cars with turbos were launched by Chevrolet (General Motors) in 1963 with their Monza and Oldsmobile F85. After that came Porsche in 1971 experimenting with the legendary Porsche 917 race car pushing power up to 1000hp This in turn led to turbo development on other race cars and then led to a turbo being developed for the 911 road car and the Porsche 911 Turbo being launched in 1974.
Unfortunately the 911 Turbo gained an image of being a difficult car to handle. With its weight at the rear end, which, in a spin would create a pendulum effect, which would be difficult to control and adding a turbo charger that would more than likely break the traction of the rear wheels on corners, it became an icon, but some times for negative reasons.

In grand prix race cars turbos have been able to force 1000hp from as little as 1.5 litres.

Later Porsche turbocharged road cars included the 924 Turbo which boasted 170hp from a 2 litre engine, later development with fuel injection got power up to over 100hp per litre in the 924 Carrera GT and this then led to the 944 Turbo in 1984. Probably one of the most famous Porsches is the Porsche 959 which itself in 1985 had a 2 stage turbo charger and this gave the 959 a massive 450hp from its 2.85 litre engine, giving 158hp per litre, no mean feat even by todays standards, and this was a road car. The 2 stage turbo allowed a little bit more control over the power delivery, and along with developments in variable vane geometry within the turbo itself this has allowed turbos to become one of the most common engine upgrades to production cars.