Every member can have their own Buddy List.
You can manage your buddies and view the list of your current buddies in your profile under "Edit Buddies".
All of your buddies on your list will be shown with their display name, and their status upon whether they are online or offline on the forum, other things like the users PM's and email address will be shown if the buddy has entered it in their profile.
You can add a Member to your buddy list straight from the Edit Buddies page, where it says "Add To Buddy List" at the bottom of the page.
Basically it is just a way to keep track of friends or people you like.