1. Every story has a mystery and plot which has an ending, but then the stories also build upon one another toward some main plot -- so you can read and enjoy one book, but also want to continue reading from book to book.
2. The characters, particularly the students, are believeable and act in a way you can imagine young people in school acting, so nothing seems "fake," even though the events are happening in a completely fantastic world.
3. There is sympathy even for the villainous and banal chracters. Neville is a weakling and bumbler, but also a hero. Snape despises Harry because he despised Harry's father -- then you discover he had good reason to despise Harry's father! Aunt Petunia is a total loss as an aunt, and yet you see that she does have some shred of loyalty to her dead sister and to Harry. It's nice the characters are presented with a human touch.