What 'mythical creature' is David searching for?

He is searching for the Blue Fairy (or the Fairy with the Turquoise Hair), the character from the Pinocchio story who first brought the puppet to life (in the Disney version of the story), and later turned it into a real boy (in both the original book by Collodi and the Disney version). David believes/hopes that the Blue Fairy can similarly turn him into a real boy too.