In any electric motor, rotation is caused by two magnetic fields that oppose each other. In some motors, both fields are created by coils of wire - electromagnets. In other motors, one field is electromagnetic and the other comes from one or more permanent magnets.
In the permanent magnet (PM) motor, the magnetic field from the permanent magnet(s) are constant (obviously) and the other field is turned on and off, or 'commutated' at just the right time so the fields oppose, causing rotation.

Commutators can be mechanical - you have probably seen the brass segments around the rotor's end that the brushes touch - this is the commutator.
In some motors, mostly small cooling fans and the like, commutation can be electronic using position sensors and switching transistors. These motors are called 'brushless'.
Since the power of the motor comes from the opposing magnetic fields pushing on each other, the PM motor is only as powerful as the magnets used in its construction. There is quite a bit of research going on to create very powerful magnets for high performance PM motors used in radio controlled cars, planes and other applications where a powerful yet small motor is needed.