From Howstuffworks.com

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 (the cylinder) 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.

The rotary engine (originally conceived and developed by Dr. Felix Wankel) is sometimes called a Wankel engine, or Wankel rotary engine

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