Which force moves the armature of an electric motor?
I assume you've read the Wikipedia and How Stuff Works articles about motors, but these just talk about magnetic attraction and repulsion without explaining the underlying physics.

The Wikipedia article on magnetic fields provides a better basic discussion about the relationships between magnetic field, the energy associated with it and the forces that can be generated.

The key concept is that motors produce torque because the tangential force on the rotor is attempting to reduce the total energy of the magnetic fields within the motor.