Putting damping material inside the subwoofer boxes serves two function: one is to smooth out the frequency response and the other is to make subwoofer hit deeper notes.

we know the subwoofer when playing music would move quite rapidly and sometimes violently when we crank it up.  The movement of cone would move air thus creating sound pressure (music), but at the same time vibrate the box too.  That’s why inside a good quality sub box you will see braces all over them to make sure the box wouldn’t vibrate.  However, because usually boxes are rectangular shape, and each walls would create a resonance frequency depending on the length.  By adding damping material in the box, you can absorb some those noises thus creating a more linear frequency response.

Another benefit is that the damping material would actually slow down the air speed in the box.  To a subwoofer, that would have the effect of having bigger boxes.  So when tuned correctly, you can make the subwoofer play even deeper bass.

Because I know putting some damping/filling material actually make very audible difference, when I install sub and amps for customer, I would actually put them in for customer without extra charge.  Just so that the customer can hear even better music. For those of you who is thinking of having the sub & amp done, I usually charge $90 for standard installs.