I skimmed the first one at B&N in twenty minutes. I've skimmed sections of the others. Personally, I found the writing to be pedestrian, but I'm not much of a fan of "fantasy" writing to begin with.
Certainly I don't believe that the quality of the story or the quality of the writing explains the series' immense and unprecedented popularity. This fact and the fact that the story revolves around a school for "Witchcraft and Wizardry" explains my interest in the books.
At bottom, I believe that this series of books is an ingeniously clever lie, the purpose of which is to normalize and introduce the occult to young children, particularly "white magic." Like all successful lies, the story contains truth. In this case, the "big lie" that is smuggled in under the superficial good versus evil story is the notion that occult powers can be used for good. Follow Dr. Eckleburg's link for an exhaustive list of examples.
The reason for the appeal of the books is three-fold. First, the books introduce in a sense the truth of "spritual warfare" to spiritually starved children. The idea of an unseen, parallel (spiritual) universe is probably a novelty for most public school-educated children. Secondly, the gnostic idea of secret knowledge (sorcery) and the idea of being one of the "select" to possess this knowledge, which is clearly evident in the books, appeals to the most deadly sin of all –pride. Finally, the series offers to children a way to gain control over reality through the use of sorcery. Any misgivings the child may have regarding the use of magic would be dispelled by the stories' endorsement of "good" magic.