Calcifer is a fire demon from Diana Wynne Jones' 1986 novel Howl's Moving Castle. He is described as "a thin blue face, very long and thin, with a thin blue nose" and curly green flames as hair. He has purple fire for his mouth, two green flames for eyebrows, and orange flame for his eyes. In the movie, he is a teardrop shaped orange flame, but in the scene where Howl moves the castle, Calcifer flares up and looks somewhat like his description in the book.
It is through Calcifer's powers that Howl's castle is able to move. The fire demon will obey only Howl, though Sophie does manage to blackmail the demon on occasion to do her bidding, sometimes with disastrous results.
Calcifer is a fallen star who was caught by Howl. Calcifer didn't want to die, so he struck a deal with the wizard. Calcifer got Howl's heart and a prolonged life, and Howl received full access to all of Calcifer's considerable powers.
After a while, both Calcifer and Howl resent the contract, but it cannot be broken. When Sophie Hatter comes to Howl's moving castle, Calcifer recognizes that she is under a curse thanks to the Witch of Waste and that Sophie has considerable powers of her own of which she is unaware. To break his own curse, Calcifer offers to lift the curse placed on Sophie once she manages to break Calcifer's contract with Howl.
Unfortunately, neither Calcifer nor Howl could directly tell Sophie what the contract was and thus she must figure it out on her own. Sophie eventually discovers what the bargain is, uses her newfound magic to give Calcifer another 1000 years of life, and to return Howl's heart. Calcifer stays with Sophie and Howl in the castle, fulfilling much the same duties as he did before, only able to come and go as he pleases. In Castle in the Air (1990), the semi-sequel to Howl's Moving Castle, Calcifer spends most of his time as a magic carpet, until Howl says his name, returning him to his original state.