Bankai is the third and final form of a Zanpakuto, currently there are 5 bankais in the game. However, you are eligible to obtain one at Meditation level 75 and player level 40 (Meditation Level 50 for Urahara Clan). After activating bankai, you'll have to wait 3 minutes (30 minutes when a quincy steals your bankai) to activate it again because of a bankai cooldown.
Click here for a list of currently obtainable Bankais.