"bamf" is referred to in the C functions of most MUD codebases. "bamfin" and "bamfout" are strings contained in a character's player file that detail what immortals look like when they appear in a room using the commands "goto" or "teleport".

When an immortal character (one of the players that are involved in the administration of a MUD, also referred to as gods) teleports themselves somewhere in a MUD, the players in the room get a message that describes how the immortal enters. This message can be funny, twisted, downright frightening (within the context of the MUD itself), in character, or just plain boring, depending on the imm's personality.

"Epsilon appears in a swirling mist."
- is an example of a bamfin. It's the default one for most MUDs. It can be changed via the "poofin" command to fit whatever you desire. An example of this is:
"poofin A blinding light shines from a rip in the space-time continuum. A small orange kitten hops out of it, followed by Epsilon, who trips, falls flat on his face, scrambles to his feet, and starts chasing after the kitten again."
The command is designed so that it's not necessary to put your name first, like an emote requires, but your character's name -is- required. The poofout command works in a manner similar to poofin, except it is used when you are leaving the room, once again by using the goto or teleport commands.

Some MUD codebases actually use the bamfin/bamfout commands instead of poofin/poofout, and some will accept either.