Back emf is explained on the UNSW Electric Motors and Generators page. This video provides evidence for back emf.
(Also available on Youtube)
Things to notice:
Back emf is an application of Lenz's law. The motion of the motion of the motor causes an induced current in the armature of the motor. Lenz's law tells us that that induced current will oppose the change that caused it. The change that caused it is the rotation of the armature due to the current applied to the motor. So, the current induced in the motor will be an opposite voltage to the applied voltage - hence it is called back emf. The back emf reduces the voltage and therefore the current in the armature so that a reduced current occurs in the armature when the motor is spinning. When the motor is not spinning there is no back emf, so the full applied voltage is not reduced, and so a greater current occurs.
There are also eddy currents induced in the armature core. These will cause a force opposing the motion of the motor, and heat. Hence energy is lost through these eddy currents. To avoid these eddy currents, the armature core should be laminated.