The black cat acts as a kind of guide and mentor to Coraline in negotiating the many hazards and pitfalls of the Other World. He's only able to do this because he can move back and forth freely between the two worlds. Unlike Coraline's mother and father, he doesn't have a separate existence in the Other World; he is one cat, equally at home in the regular, everyday world and the Other World.
The cat's vast experience of moving back and forth between the two worlds makes him the ideal companion for Coraline as she attempts to free her parents from the evil clutches of the Other Mother. Though the cat is remarkably brave in standing up to the Other Mother, his courage hides an overwhelming fear that she will imprison him in the Other World forever. However, it is only by confronting such fears that the black cat is able to assist Coraline in getting her parents back.