The dog is almost always around Saya, watching over her though he doesn't like to be petted. The dog has a mysterious kind of air.

Spoiler

It is later revealed that the dog is really Kimihiro Watanuki, the protagonist of xxxHolic, who has taken over the form of a dog temporarily so that he could grant Saya's wish, though it is not initally revealed what the wish is, or who made the wish.