Here it goes my opinion (and apologise if I'm repeating what the others already said
)
I think that HP, in general, is a great "recipe" to success, from the beginning...
In the modern society, what do we all want (young and old people) ? That's easy: simply a way of getting out of that routine. And a book that is related with fantasy, and with our deepest desires (who wouldn't like to have magical powers?!), is a great way of doing that. Besides, people don't want to think much - that's a fact (no offense) - because they get home, in the end of the day, tired from their works, from the endless traffic, and so on. They want something that has the power of "transport" them to another world, and that allows them to "fly". Magic is just the perfect way, because it makes part of almost every culture's folklore.
On the other hand, it's very easy to imagine places like Hogwarts or the Platform 9 3/4, because they "exist" associated with real places, that are just so real that they are located in one of the capitals of the world (at least one of this exemples is)!
And we have still the fact that those are "normal" people, with problems, just like all of us. That allows the readers to forget their problems for a few moments, and to concentrate on the ones of the characters.
In addiction to all this, we also have what I like to call of "model characters", just like Ron or Neville. Ron is the tipical character, who makes us laugh a bit during the reading. And Neville is the kid who is absent-minded, keeps loosing his personnal things, and he isn't very good in anything: he's the kid with whom everyone is always joking about.
I hope the text is not too confused...