What is Counter Electromotive Force (Back EMF)?

Counter electromotive force (CEMF or back EMF) can be thought of as a secondary induced EMF, produced by a primary EMF, which is caused due to a changing magnetic flux.

Wikipedia defines CEMF as:

"the voltage, or electromotive force, that pushes against the current which induces it."

Consider an example:

A C-shaped conductor is placed in a static magnetic field (whose direction is in the -z direction) as shown below. A conductive bar is placed near the edge of the C, and is forced (externally) to slide in the +x direction while the C is not moving.

The two conductors together form a closed loop, and sliding the bar increases the area of this loop. By Faraday's Law, B.dS is increasing and thus (since nature tends to resist such changes) a magnetic flux is induced in the coil whose direction opposes that of the original field. This means a current flows in the counter-clockwise direction.

Now, let us consider the bar when the current is flowing. We also know that the Lorentz force states the following:

So, a second force is induced due to the induced current which was caused by sliding the bar in the magnetic field. This force opposes the force that slides the bar. This is an example of back EMF.