Batman 666 is an alternate version of Damian Wayne from a future where he takes on the mantle of Batman after he failed to save Dick Grayson, the second Batman. So Damian made a pact with the "Devil" in exchange for immortality and healing abilities he felt he needed to protect Gotham City.
The Batman 666 concept was created by Grant Morrison and Andy Kubert, first appearing in Batman #666 (2007).
Multiverse
The New 52
Possible Futures
Other Media
Comics
See Also