These are usually cubic wooden cabinets (same MDF material as speaker cabinets), which are equipped with a bass reflex port, have no diaphragm and are tuned to a specific frequency (e.g. 40 Hz as in a subwoofer). The frequency to be tuned can be changed by the length and diameter of the bass reflex port. For example, if a room has a room resonance frequency of 28.3 Hz and this frequency is also reproduced by a loudspeaker/subwoofer, the room will begin to resonate at this frequency. This particular frequency is reproduced amplified.
You can think of it as a boom or thump that occurs during bass-heavy movie scenes like explosions or certain types of music (jazz, plucked bass). The bass absorber is then tuned to this exact frequency so that only the speaker/subwoofer reproduces this frequency. The resonant frequency of the room, which would amplify this frequency, is swallowed by the bass absorber.
If you want to attenuate more than one frequency - a room usually has three different frequencies (ceiling and floor, front and back, right and left) and their multiples - you have to set up three absorbers accordingly.