After rereading Harry Potter I felt there were a couple things that made HP as popular as it is.
Firstly: Just the obvious stuff, it didn't suck. It was competently written, the characters had personalities, it had a mix of humor and serious moments. Even the movies were competently done.

Secondly: The world JK created. Hogwarts is such an appealing wonderful place, and JK does an amazing job writing and creating the world. Simply namedropping things like The Daily Prophet and using Harry to explain how the wizarding world works, JK was able to create an appealing world. I think people could see themselves going to Hogwarts. Hell there's a website where you can take online Hogwart's classes. If that doesn't show the appeal of the world itself (not the characters or the plot) I don't know what does.
I feel these aspects made HP popular. But it is the next aspects which took HP over the top and made it one of the best selling books of all time.
It's progression. Specifically it was able to take to grow at about the same pace as its readers. As the main characters grew up and new books were released the readers of it grew up. Having a growing up tale that parallels the readers growing up, having each book get more "mature" is an opportunity very few books have. And this sort of experience no other readers are going to be able to get from the books.
The last aspect that made HP as popular as it is today is its popularity. This might sound redundant but its extremely relevant. Events like the opening night release of the next book or movie, were very special and the only reason why these occurrences were able to become the EVENTS they were was because HP had an established popularity. These events added to HP's popularity. Even if the book wasn't as good as you liked you could still remember the fun you had at the event, Whether it was a book release, or a convention, or whatever.