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.
Like a piston engine, the rotary engine uses the pressure created
when a combination of air and fuel is burned. In a piston engine,
that pressure is contained in the cylinders and forces pistons to
move back and forth. The connecting rods and crankshaft convert the
reciprocating motion of the pistons into rotational motion that can
be used to power a car.
In a rotary engine, the pressure of combustion is contained in a
chamber formed by part of the housing and sealed in by one face of
the triangular rotor, which is what the engine uses instead of
pistons.
The rotor follows a path that looks like something you'd create
with a Spirograph. This path keeps each of the three peaks of the
rotor in contact with the housing, creating three separate volumes
of gas. As the rotor moves around the chamber, each of the three
volumes of gas alternately expands and contracts. It is this
expansion and contraction that draws air and fuel into the engine,
compresses it and makes useful power as the gases expand, and then
expels the exhaust.