A monopod works on rotational inertia, which is a function of length squared (assuming uniform mass density). While nowhere near as stable as a tripod, a monopod should do better than holding a camera in your hands (especially if it is heavy).
For a neat example of rotational inertia and the function of length, try to balance a normal pencil in your hand, with the eraser in your hand and the point oriented upward. It's almost impossible to do.
Now take a yard or meter stick and try the same thing. Hold one end in the palm of your hand with the stick pointed upward. It's actually pretty easy to maintain an upright orientation.
The yard/meter stick has a high rotational inertia whereas the pencil does not.
A monopod will eliminate considerable motion. Up and down motion is essentially zero. Longitudinal (forward/backward) motion is probably negligible. Lateral motion (left/right) is minimal, though not eliminated. Pitch should be essentially gone, as well as yaw. Roll is a function of the degree to which you have lateral motion, but again this should be minimal.
While you wouldn't use a monopod for long exposures, it's probably a very nice tool for situations where you want a steady camera.
Hope this helps!