BNC is somewhat short for Bouncer in the irc langugage. Its mostly used to get a nicer looking host or to hide yourself from something. They are also a good semi-replacement for irc robots, bots because some of the bouncers are on irc all the time, even when the original user has disconnected.

The popular irc bouncers include:

muh -
psybnc -
ezbounce -

(these links may vary with time)

Bouncers are offen run on shell servers. Some rootkits allso contain some version of psybnc.