The process of amplifier damping is explained with excerpts from a paper written by Dick Pierce, Damping Factor: Effects On System Response. Mr. Pierce's area of expertise is in professional audio development.

Source: Dick Pierce
Date: 1998-2002
In his introduction, Mr. Pierce states that much ballyhoo surrounds the concept of "damping factor." It's been suggested that it accounts for the alleged "dramatic differences" in sound between tube and solid-state amplifiers. Also, many of the claims made, especially for the need for triple-digit damping factors, are not based in any reality, be it theoretical, engineering, or acoustical.

What is damping factor? Simply stated, it is the ratio between the nominal load impedance (typically 8 ohms) and the source impedance of the amplifier. Note that all modern amplifiers (with some rare exceptions) are, essentially, voltage sources whose output impedance is very low. That means their output voltage is independent over a wide range of load impedance.

Mr. Pierce ran an analysis of the effects of amplifier damping factor on the decay time and frequency-dependent response of a closed-box, acoustic suspension loudspeaker system. The results were that any damping factor over 10 resulted in inaudible differences. Calculations suggested that a damping factor in excess of 50 will not provide audible improvements. Also, for audio power amplifiers employing global negative feedback, the source impedance is generally smaller than 0.1 Ω.

Comment:
At 0.1 ohms (Ω), with an 8-ohm speaker, the damping factor would be 8 divided by 0.1 = 80. The paper written by Mr. Pierce has a copyright statement concerning distribution of the paper and although a copy is on file, it is not provided here. If you search, you can find more information on Mr. Pierce's paper.