Amplifier Damping Factor is a measure of the amplifiers ability to control the cone of a speaker. It is a required element in all amps, for all speakers, although electrostatics may differ in need.
Technically, a speaker is an electric motor with in and out motion. This motion also turns the speaker into an electrical generator. When the electric signal (sound) is applied to a speaker which moves in one direction, and when it moves in the opposite direction can produce voltage. This is because of the voice coil moving throught the magnetic lines of flux of the speakers magnet. This voltage is sometimes called "back voltage".
If the amp has a relatively low internal impedance, it will act as a short circuit on the back voltage. This will act as a brake and stop, or slow the cone motion after the original signal has ended.
That is my understanding of damping.