What benefits does it have? and what exactly does it do?
i just built a sub box and someone suggested putting the insulation inside the box.
Pollyfil is a sound absorption, dampening fiber that will deepen bass, provide cleaner midrange, tone down any unwanted reverberation and improve the dynamic extension of any speaker system.
It also helps eliminate standing waves, which is something like an echo inside the box. This will give you tighter and more accurate bass. It also helps to give a flatter frequency response to the overall sound, which is good. Besides this, it also helps reduce the vibration of the box, which results in less distortion. There is a big difference to the bass when you have an insulated box.
Damping also increases subwoofer efficiency by dissipating some energy that affects the sub, particularly the voice coil. It is advisable to put damping material inside a box. Pillow polyfill and fiberglass insulation are common, though polyfill is a lot easier on your skin. Polyfill also “tricks” a sub into thinking it is in a bigger box. Most sealed and vented enclosures require 1/2 lb. of dampening material per cubic foot of internal enclosure space. For best results it is recommended to loosely fill the material throughout the enclosure.

it 'tricks' the box into thinking it's bigger i believe. but you sacrifice some output. i wouldnt do it to any of my boxes.
References :
Articles I've read stated it was to prevent the sound from "leaking" out the back of the enclosure.
References :
I believe you're talking about polyfil, the cotton-looking stuff. This substance, essentially, slows down the sound waves as they pass through it, making the subwoofer think it is in a larger box than it really is, because the sound waves take longer to move around. The benefits of this is, obviously, if you build a box that is too small and you don't want to make a new one, put some of this in.
References :
Pollyfil is a sound absorption, dampening fiber that will deepen bass, provide cleaner midrange, tone down any unwanted reverberation and improve the dynamic extension of any speaker system.
It also helps eliminate standing waves, which is something like an echo inside the box. This will give you tighter and more accurate bass. It also helps to give a flatter frequency response to the overall sound, which is good. Besides this, it also helps reduce the vibration of the box, which results in less distortion. There is a big difference to the bass when you have an insulated box.
Damping also increases subwoofer efficiency by dissipating some energy that affects the sub, particularly the voice coil. It is advisable to put damping material inside a box. Pillow polyfill and fiberglass insulation are common, though polyfill is a lot easier on your skin. Polyfill also "tricks" a sub into thinking it is in a bigger box. Most sealed and vented enclosures require 1/2 lb. of dampening material per cubic foot of internal enclosure space. For best results it is recommended to loosely fill the material throughout the enclosure.
References :
A.A.S. degree in Electronics/Industrial Electronics with 25 years in the mobile audio/consumer electronics field