If you've ever looked at a performance car's specifications and wondered what “turbocharged” or “supercharged” actually means, the basic idea is surprisingly simple. Both are ways to force more air into an engine. More air allows the engine to burn more fuel, which can produce more power from the same basic engine size.
The big difference is how they get that air moving. A turbocharger uses exhaust gases to spin a turbine, while a supercharger is driven mechanically by the engine, usually by a belt. That one difference creates very different driving characteristics.