Jack Napier is a criminal who later fell in a vat of chemicals that made him become The Joker. Jack Napier was originally in the Batman 1989 movie portrayed by Jack Nicholson, but He appeared in The animated batman movie, Batman: Mask of The Phantasm. He also appeared in The New Batman Adventures, in a flashback in the episode "Mad Love". In The New Batman Adventures they claim The Joker's identity is unknown, but it is probably because Jack Ryder doesn't know who The Joker really is.
It should also be noted that in Batman: Mask of the Phantasm the Joker's former identity is never referred to by this name. He is only ever referred to as Jack Napier once in the first Batman: The Animated Series. The reason for this is often suggested to be that the the cartoon was heavily patterned after the look and tone of the Batman movies of the time. This is logical since the true identity of the Joker in regular comic book continuity is to this day not known for sure.