The motor uses the electricity to make temporary electromagnets. There is a ring of these magnets around the case of the motor, there are some on the rotor, the part that spins. The motor supplies power to one of the magnets around the case also to one of the magnets on the rotor. The two magnets are now attracted to each other, the magnetic power pulls the rotor towards the case magnet. Before it gets to the point that the two magnets are lined-up, it turns the case magnet off switches power to the next case magnet, that is just a bit further away. The magnet on the rotor is now attracted to the next one, the rotor is pulled around a bit further. The motor then switches the power to the magnet that's next around the case, the rotor continues to turn to try get the magnets to line-up. It's a bit more complex then that, but that should give you the general idea.
Hi it works by using the alternating currents causes flux changes which cause rotation of the field and stator currents. hence rotation the stator can be a laminated solid armature as the field rotates around it. unlike a dc motor where the commutator does the switch with the brushes.
