Part of the attraction of Harry Potter and the Philosopher's Stone comes from the familiar but at the same time exotic setting of an English public school, complete with houses and schoolboy adventures, in which Harry and his friends Ron and Hermione struggle to save the world and win the house cup. Part of it comes from the pleasantly frivolous (verging on spoof) take on the trappings of pop magic, with pointy hats and "Nimbus 2000" series broomsticks. And Rowling adds some delightful novelties of her own, such as Quidditch, a seven-a-side ball game played on broomsticks, with three different kinds of balls. This is all pulled together by some excellent story-telling.
I can't understand, however, why quite so much fuss has been made about the Potter books. To highlight the limitations of Harry Potter and the Philosopher's Stone, it is instructive to compare it with another children's fantasy novel in which a neophyte wizard attends a school for wizards — Ursula Le Guin's A Wizard of Earthsea. This works just as well as a story, but it displays invention of a qualitatively different order. Where Rowling reworks superficial popular ideas about magic in an ad hoc fashion, Le Guin constructs a fully-fledged, but consistent and coherent, world of her own: dragons in Earthsea, for example, are both an integral part of the imagined world and anchored to mythological precursors; for Rowling they are just a plot device appropriated from common cliche. Le Guin cuts far deeper, too, in dealing with such subjects as coming of age and acceptance of mortality, and her protagonist is rounded in places where Harry Potter is no more than one-dimensional.
So Harry Potter and the Philosopher's Stone will be a great Christmas present for kids who haven't read it yet — and it is a book that adults (at least those without stunted imaginations) can read as well. But A Wizard of Earthsea is all of that and more, and children's fantasy is a reasonably well-populated genre, so don't let the hype surrounding the Harry Potter books hide the other goodies out there.
Addendum (since people keep mailing me to tell me I have it wrong): Harry Potter and the Philosopher's Stone is the correct title of this book, as chosen by Rowling and used in the British edition. Scholastic, the American publisher, changed it to Harry Potter and the Sorcerer's Stone, even though the Philosopher's Stone features prominently in alchemical tradition and "the sorcerer's stone" means nothing.