He is the leader of the Dark Judges, a sinister group of undead law enforcers from the alternative dimension of Deadworld, where all life has been declared a crime.
The full story of his journey from being Sidney D'eath, the son of a sadistic travelling dentist, to his incarnation as a creature of pure evil is recounted in the Judge Dredd Monthly series Young Death- Boyhood of a Superfiend.
The representation of Judge Death in the Judge Dredd and related comic strips has changed somewhat in character over the years. In his first appearances his image was extremely dark and sinister, with a real air of menace. However post Necropolis stories have tended to present him in a much more humourous light. For instance in the Judge Dredd/Batman crossover graphic novel Judgement on Gotham Death was used as a practically comical figure.
See also Judge Anderson, Sisters of Death, Necropolis