mass loading - making the structure heavier and more stable relative to the diaphgram in the driver; heavier the better usually, but since we still need comfort there has to be a compromise somewhere
(mechanical) vibration damping - certain materials absorb mechanical vibrations in the structure better than others; oftentimes these add a bit of mass loading as well
acoustic damping - certain materials absorb/reflect sound waves better than others
The first two primarily contribute to making the driver more stable, thus leading to a cleaner response. The last one affects how sound eventually reaches your ear.
The simplest/cheapest way to mass load is to use some putty (poster/plumber's putty, plasticine, etc). Fancier stuff would be vibration absorbers like dynamat, but those are generally more difficult to work with and often cost prohibitive to obtain in small quantities.