A turbocharger uses exhaust energy to spin a compressor that forces air into the engine. Since more air is entering the engine, you can add more fuel, and the more air-fuel mixture you can cram into the cylinder, the more power the engine will produce.

The turbo has two sections. The "hot" side is a turbine wheel that is in the path of the exhaust gasses. Hot gasses blow over the turbine and cause it to spin. The turbine is connected by a shaft to the "cold" side, which houses a similar wheel. That compressor wheel is turned by the shaft, and it blows air into the engine.

The whole setup is quite elegant, because it uses energy that is normally wasted -- exhaust would just flow out the back of the car. And at low engine speeds or loads, the turbo is not active, so the engine can have normal-use fuel efficiency just like any other small four-cylinder. Then at high loads, the turbo spins up and turns it into the equivalent of a V8.