In photography, B is a shutter setting. When a shutter is on B, it will remain open as long as the release button is depressed; combined with a suitable locking remote release, it allows one to take very long exposures, longer than what the shutter would allow by itself.
I think that digital cameras typically do not have the B setting.
B stands for bulb, but what bulb are we talking about? I have read two theories for the origin of the word; one is that this is about flashbulbs, while theory two refers to the air bulbs that one finds at the end of pneumatic remote release cables. The first one sounds more convincing to me, dating back to an era when you did not have synchronized shutters.
See also:
shutter,
exposure,
T and
X.