Damping is about the ability of an amp to control the movement of a driver when no signal is send.
Floyd E Toole describes a nice and simple experiment.


Take a driver, preferably a woofer.
Have it disconnected so no electromechanical damping at all.
Gentle pressure on the diaphragm will move it easily back and forth.
Now shortcut the terminals with a wire and apply this pressure again.
This time the  diaphragm will offer a kind of viscous resistance to movement.


Basically, a speaker can work like a microphone.
If you move the diaphragm, the voice coil will generate a current.
If you shortcut this current you will limit the vibration (ringing) of the diaphragm, indeed this is damping.
The lower the impedance of an amp compared to the impedance of the driver, the better the damping.


Damping factor
The damping factor of a system refers to the ratio of nominal loudspeaker impedance to the total impedance driving it (amplifier and speaker cable).
Of course bigger is better but is it?.
NwAvGuy advise is to have a damping factor of minimal 8.
Floyd E Toole recommends 20, like wise Dick Pierce argues that 20 is more than sufficient.
 John Sia argues that 10 is way to low, 100 is better and 200 a value to aim at.


Low damping.
This occurs if you combine an amp with a high output impedance with a headphone with a low impedance.
This can happen if the headphone out of an amp is simply the output of a poweramp (the speaker terminal) with a big resistor in place hence a high output impendance.
Likewise modern headphones can have a very low impedance making them easy to drive by amps frugal on power (portables).

This combination will generate a very bloated bass.



Damping, damping factor and damn nonsense - Floyd E Toole
Headphone & Amp Impedance - NwAvGuy
Damping Factor: Effects On System Response - Dick Pierce
Audibility of Low Damping Factor?

Damping Factor - Sweetwater