Calcifer is a falling star that Howl caught and gave his own heart to. This contract keeps Calcifer alive but binds him to the castle’s hearth.
Sophie is the only person who treats Calcifer like a sentient being rather than just a tool. Her care (feeding him quality wood, praising his "spark") directly correlates to the castle's strength and stability.
The central mystery of the film involves breaking the curse that binds Calcifer and Howl.