I need an explanation of "damping factor".

Help me out here with the spec of "damping factor", and how this relates to bass control. For example, most Mac amps with the autoformers have a damping factor of 40. My MC7200 is rated at 200, but my Adcom 5500 is rated at 700. At what point does this spec become meaningless? Thanks for any help!
The damping factor is the output impedance of an amplifier, divided into the speaker impedance. If the amp's output impedance is 0.5 ohm, and the speaker impedance is 8 ohm, then the damping factor is 16.

It is typically discussed in terms of the control the amplifier has over the speaker cone excursion. It is primarily important in the bass response, where the cones are at maximum excursions.

The levels of damping factor importance are subject to opinions. Some damping factor is required, or the amp will oscillate, which will happen if the speaker impedance drops below the amp output impedance.
When an amplifier sends a signal to the speaker, the electrical signal energizes the coil and causes the driver to move. When the signal stops, there is no more electrical energy to the coil; however the driver keeps moving through inertia - it cannot stop on a dime. This unwanted movement causes the driver to now act like a microphone, it moves the voice coil through the (permanent) magentic field which causes a back-voltage to the amplifier's output. In order to prevent this back-voltage, the amplifier should present a short to the speaker's perspective. So the amplifiers' output impedance has to be very small, including that of the speaker cable in order for the driving impedance to be as close to zero (short) as possible.

The damping factor is the amplifier;s ability to prevent this back-voltage, or unwanted driver movement. It is the ratio of the speaker impedance to the total impedance driving the speaker. An amp with an output impedance of 0.01 ohms driving a speaker with 8 ohms will have a damping factor of 800 (8/0.01). But - you have to add the resistance of the speaker cable for the total driving impedance. If the cables have a high resistance, this decreases the overall damping factor. For example: amp output impedance 0.01 + 0.79 cable impedance = 0.80 driving impedance which is, to an 8-ohm speaker, 8/0.80 = 10 damping factor. So the speaker cables add to this effect.

This spec becomes "meaningless" after a factor of 10. A ten to one ratio between driving impedance and speaker impedance will adequately control the speaker cones. Is one amp with a higher damping factor better than another with a lower one? Not necessarily - there are many design parameters for amplifiers in addition to damoing factor.
Thanks to both Twl and Gs5556 for the excellent explanations. I love it when I learn something :-).
I concurr. Knowledge is a wounderful thing. Thanks for the explanation.
Thanks to all of you for the helpful info.