As far as what the filters do goes... they help to reduce the effects of stored electrical energy within the speaker causing negative interactions with the driving amplifier. The amp and speaker are really a "system" and it can be a very complex one at that. The amp has enough "work" to do in sending the signal to the speaker to begin with. If it also has to contend with delayed energy being sent back to it from the speaker, that energy can cause the amp to make new "errors" (distortion).
Thanks for your explanation Bob, I found it very helpful in understanding more about how your product works. Regarding the above quote, is what you are describing here known as EMF or back wave? I use a set of pig tails made by Creative Cable Concepts that I place on the positive binding post of both the amp and speaker. Their purpose is to reduce EMF/back wave energy. I have noticed a lowering of the noise floor and smoothing out of the sound as you describe.
Another question, how does your product differ from products like the Walker speaker filters? I use a DIY version made by a friend of mine and the effects are positive, similar to the effects users of your product describe. I'd be curious if your product operates on similar principles.