Acoustic treatments are used to alter the sound dynamics in a room.  Acoustic treatment might be necessary because of dead spots in a room (areas with little volume), too much reverberation in a room, or uneven frequency distribution in a room.

There are three types of acoustic treat.  These are absorbers, reflectors, and diffusers.

Absorbers are used to attenuate (lower) sound levels.  Absorbers are typically made of porous material.  The thicker the material, the more it can absorb.  Absorbers work by transferring sound energy into heat.
 

Reflectors are used to reflect / bounce back the original signal with a limited loss of energy.  Reflectors would bounce back the sound into other areas of a room, possibly including the direction of the initial sound source, depending on the type of reflector and the reflector setup.  They might be used to resolve dead spots or increase the sound strength.  For example, using reflectors in a orchestral theater to re-direct sound back towards the audience instead of up to a very high ceiling.

Diffusers are used to diffuse (I so hate using the same word to define a word) or "scatter" sound.  They send sound waves in many different directions. This is good if you don't want an entirely dry room, but want some sound "reflections" for recording, say, drums.  The more expensive diffusers send audio waves in different direction based on frequency.  Diffusers are used for reducing standing waves and echoes.  I think this diffuser looks like something from Star Wars.