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 - http://mind.riot.org/muh/
psybnc - http://www.psychoid.lam3rz.de/
BNC - http://bnc.ircadmin.net/
ezbounce - http://druglord.freelsd.org/ezbounce/
(these links may vary with time)
Bouncers are offen run on shell servers. Some rootkits allso contain some version of psybnc.