Plenty of movies have narrators. In very few of those does the narrator also get to be an actual character in the story. Lucky him.

From the get-go, we're introduced to the sick (OR IS HE???) grandson and his grandfather, who comes to pay him a visit and read him a book. He's sweet, and patient, and he's played by Peter Falk, so he's just got that voice that makes us want to hear whatever he's got to say.

Once he begins reading the book to the boy, he also begins reading it to us, and serves as our narrator for the remainder of the film. He only pops in from time to time, and usually it doesn't even sink in that we're listening to a narrator, since we're totally used to the whole "once upon a time"-type voice when reading/listening to fairytales anyway. It fits with the style of the story, so it doesn't stick out like a sore thumb. Or, in the case of the six-fingered man, like an extra one.