As has already been said, they vary.
An electric motor generally uses electromagnetism to create motion. If current goes through a wire, it creates a magnetic force. If a wire moves through a magnetic field, an electrical current is produced in the wire. Both of these physics concepts are leveraged (pun intended) to get the axle moving. What you'll find inside a motor are a number of windings of fine wire around a metal slug, and some magnets arrayed around the case. Some motors are "inside out" with the windings on the case and the magnets in the middle. The rest of the motor is just the use of ball bearings or pin bearings to allow the axle to turn, and some form of contacts to allow current to be applied to each winding or to detect when current is generated from the motion.