The Buddy List displays all of the members on the TTB forum whom you have added as a “buddy”. The list shows their online status and contact information, if the member has made that information visible.
Basically, buddy lists make it easier to send PM's to people and see who's online by a little green (online) or grey (offline) icon.
Other than that, I have never been able to find more informative documentation to support or refute its benefits. If I find anything new, I'll add it to this post.
You access and edit your Buddy List through your Profile page.