I very much agree with flightywoman. I thought they rather cleverly combined different genres. They're a bit like good crime fiction - every plot has a driving narrative with a mystery to be solved, and a final, usually surprising, twist.
They also resemble traditional kids' boarding school stories - Malory Towers and the like (but better, in my view).
They have a CS Lewis-style magical world feel too - the influence of Narnia is obvious, but without the tedious religious element.
On top of that, I admire them because she has managed to convincingly create this whole alternative imaginative universe, which is quite rare, I think, even in kids' books. There's lots of cleverness with language - if you know even a bit of Latin or any romance language, you'll enjoy the terminology she comes up with for the various magic spells and characters' names.
The characters are strongly drawn, which I think has to be a prerequisite of any good kids' books.
There's quite a bit of gentle humour, but also a lot of reflection on quite tricky moral issues, such as whether it's OK to use Dementors (essentially evil beings) to guard dangerous, high-security prisoners.
Finally, she rather brilliantly maintains a complicated narrative arc over all seven novels, as well as having a self-contained plot with twists and turns in each novel individually.
I know some people say she's not a brilliant prose stylist, and that's true. They also say her characters lack psychological depth, which is probably also true. But she does the rest so brilliantly I would find it very hard to hold those things against her.