This term is sometimes used to denote that a user is present but essentially AFK (away from keyboard). This usually applies when somebody is playing a game, watching a movie, or doing something else that prevents them from being able to receive and reply to some form of messages within a reasonable period of time.
User: Hey guys, I'll have to catch you later.
<<User changes his/her nickname to User|HBAFK.>>
User: I'm going to go hbafk while I play some Day of Defeat.
OtherDude: Ok, see ya.