A bus is a way of putting many audio tracks through a mixing desk on to one fader (or track in Adobe Audition / Pro Tools). It enables you to control everything in one place. AUX sends (or just sends in Adobe Audition) will then isolate one sound from your mix and send that clean sound (with no other sounds from your overall mix) into something else. Like perhaps a dynamics processor.

A real world example of using an aux and bus would be so that you can get a voice over to automatically control a music track by ducking it every time speech is heard.

Adobe Audition YouTube tutorials: http://www.youtube.com/user/musicradiocreative