This is about the anime character. For the monster itself, see Cinder Bird.
Cinder Bird appears in the anime series as the Phoenix's first form when it is revived. After its body has been frozen for years and its mind separated, it cannot reignite its flame until the spirits of the Searchers combine forces.
The Jills tell the Searchers an ancient legend about how the Cinder Bird once showed kindness to their village and saved it from the evil Skull-Capped. After that, it had a special bond with their village and is perhaps the reason why it ended up frozen nearby.