Audition is Adobe's sound editing program, making a return to the Production Studio with CS5.5 and replacing Adobe Audition (which did the same kind of things but with a simplified interface). If After Effects is for making complex things with pictures, Audition is the same thing for sound.
There is a “dynamic link” between Premiere Pro and Audition - you can send a Premiere timeline to audition and the software keeps all the audio edits intact. Once finished you send the final mix back to Premiere Pro where it slots back into the timeline from where it started.
Why use Audition to do audio effects you could achieve in Premiere?
Because you can take them a step further and the quality is better. The noise reduction in Audition is light years ahead of the simple noise filter in Premiere, for example.
Audition has several tools to improve the quality of your sound. Sample a sound, like a microphone buzz, and remove this sound through the entire file. Or use Audition’s spectral view to isolate and lasso a sound and then remove just that sound from a clip - select the screech of a seagull or the creak of a door and just remove that whilst leaving the rest of the sound intact.
Audition’s music abilities can take "loops" of sound and you can lay them out as a piece of music. You can even take your own sounds and make them loopable. Not as easy as the instant music creation of Soundbooth but still easier that actually writing music.
Lots of filters
There are a huge number of filters for tweaking, EQ, pitch shift, time stretch and more.