Damping factor is such a debated and oft-misunderstood specification.
Essentially, it is the source impedance of the amplifier, divided into the load impedance of the speaker. It has nothing to do with feedback in the amplifer. It has to do totally with the source impedance of the output stage (how much current the output transistors can sink) and the source impedance of the power supply (how much capacitance and how well-regulated it is--sometimes referred to as "stiffness"). Typically, amplifiers with huge supplies and a lot of capacitor reservoir storage and numerous output devices in parallel will have high damping factors. My old Phase-Linear D-500 had 32 output devices and boasted a damping factor over 1,000. My current QSC Powerlight amplifiers claim in excess of 4,000 for the damping factor.
Damping affects the degree of control over the 'motor' of the speaker--the voice coil/cone assembly in conjunction with the magnet. When the cone is coasting, it becomes an electrical generator, producing back-EMF (electromotive force) that is being sunk back into the amplifier. A high damping factor resists this back-EMF and provides more braking action on the cone. It follows the input electrical signal a bit more accurately this way.
The effect of various levels of damping will be more or less noticed depending on the type of speaker system in use. Sealed baffles will see the least change, as will horn-loaded systems, since most of their damping is mechanical. But open back (no longer seen in today's mainstream) and vented systems will be more dependant on damping in the electrical domain, because they have mechanical damping that varies with frequency, especially around the vent tuning frequency.
Electrical damping can only be somewhat maintained in biamped systems, where the woofer is directly connected to the amplifier, with no components in between, including inductors, fuses or circuit breakers. The use of heavy (I recommend 8awg) cable helps to maintain the low source impedance of a super-class amplifier, at the speaker terminals.
The effects of damping on sound: Low damping, due to insertion loss (inadequate wire gauge, resistors, inductors) results in a fatter, 'tubby' bass with less definition. By eliminating the IR losses in the wiring, a more accurate, less resonant bass is the result, but many will also perceive this as a loss of bass. Indeed, by eliminating the overshoot, the bass energy at SOME frequencies will be reduced, but to the gain of quality and smoother response. I experienced this phenomena when I replaced my 14awg home brew cables (which were heating up during loud playback) with 8awg cable. The bass seemed less powerful after that upgrade, but I eventually realized that the system response was also smoother and bass notes no longer 'ring' after the note is stopped. So if you're expecting louder bass with heavier cables or more damping, don't. But if you're after better impulse response, then DO upgrade the amperage capacity of your cables and use high damping amplifiers.
Bob Carver made the "t" (Transfer Function) modification to some of his solid state amplifiers and last year at CarverFest, he revealed what 80% of the transfer function mod (to make it sound like a tube amp) was: insertion of 1.6-ohms of resistance in the output of the amp channels. By inserting resistance between woofer and amp, you'll simulate much of the 'warm' sound of tube amps.
