Like a balloon, a rocket engine in its simplest form is a chamber enclosing
a gas under pressure.
The pressure is provided by the combustion (burning) of the fuel and
oxygen (oxidizer).
The resultant combustion gases then "escape" through a hole (nozzle),
thereby propelling the rocket/chamber in the opposite direction.
Rockets, from air-to-air missiles to the Space Shuttle's main engines,
are basically the same and differ primarily in size and complexity of
the engine hardware.