This is perhaps the most common device used in fantasy fiction. It's not really that surprising, when you think about it. Many people read fantasy as an escape from a reality in which they find themselves stymied or powerless (perceived or actual) to change or improve their lives as desired. Thus a hero who rises from modest origins to do great things evokes a sense of pleasure in the reader, who can enjoy the fantasy that they, too, may someday rise from their own limited situation to accomplish great things. Particularly popular seems to be the hero who appears to be a "nothing" but then develops some abilities/magic that transforms him into someone who can shape the world around him/her. Sometimes the transition is so rapid to be almost jarring (at least to me), such as in Feist's Magician, when the hero goes from being a total wimp to a super-power mage very quickly. I don't think I ever finished that one. Ditto for the Sword of Truth series, where the hero starts out as a "humble forest guide" (TM) and turns into this avenger-type with the Ultimate Artifact who also happens to be the son of the most powerful leader in the world.
Sometimes the link between Reader and Hero is even more direct; there are several fantasy series where the protagonists are modern humans (i.e. from our world) who are placed into a fantasy setting. See Rosenberg's Guardians of the Flame and Guy Gavriel Kay's Fionavar Tapestry for example.
As you can guess from the tone of the above, I'm getting a bit tired of this particular literary style. I think it can be done in a way that isn't overbearing; for example I enjoyed GG Kay's Sarantine Mosaic duology, although the characters in that one also go from insignificance to prominent positions in the circles of power in the Empire's capital city.
This is the same phenomenon that drives the success of lotteries and game shows, IMO.