A .bic file is a Neverwinter Nights character file, used to store name, race, class, deity, feats, spells/invocations, inventory, etc. There are several premade, and a new one is created in the localvault whenever a character is created.
Important Online Information Edit
In persistent online worlds (servervault) these files are stored by the host machine, characters in these modules who carry huge numbers of items in Bags of Holding will crash more frequently during area transitions and can even cause the server itself to crash.
A guideline of keeping bics under 900,000 Bytes works well, although even smaller is better. Most of this comes from inventory. You can export locally to see your character's size. It will show up in localvault.
Over 2,000,000 Bytes is a crime against any online server.