A rotary engine is an internal combustion engine, like the engine in your car, but it works in a completely different way than the conventional piston engine.
In a piston engine, the same volume of space alternately does four different jobs — intake, compression, combustion and exhaust. A rotary engine does these same four jobs, but each one happens in its own part of the housing. It’s kind of like having a dedicated cylinder for each of the four jobs, with the piston moving continually from one to the next.
When it was first conceived it was referred to as the Wankel engine in 1929.
This animation provides a basic understanding of how the Rotary Engine is put together and how it works.