Its main feature is its simplicity, both in terms of its interface and the code used. The idea its creators had in mind was that it shouldn't look like part of a CMS.
Just like in WordPress, it's supported with templates you can use to modify its appearance. If you're not into a look, just change it.
Another important advantage is its Akismet-based architecture, which provides efficient protection against spam and other junk mail.
You can also add new features thanks to its system of plugins – and share the extensions you make yourself with other users.
Finally, bbpress lets you add RSS syndication to your message boards so nobody misses any of the latest content under discussion on your threads.