Calcifer was a falling star who made a contract with Howl and now runs his moving castle for him. His biggest fear is being extinguished, since he's a flame demon and that would mean death.
Calcifer holds Howl's heart, which makes him stronger than one of the strongest wizards in the land. But Howl's control over Calcifer means he can't leave the moving castle. It's a two way thing.
Calcifer likes wooden logs, eggs shells, bacon, and all sorts. He isn't a fussy eater. He can't stand water though. Cleaning ladies are his arch nemesises.