Fortunately, I had watched the previous movie on DVD recently, so I wasn't lost in following the story. It really is the second half of the same story, as it picks up right where the last one left off. I'm not going to review the movie, but I do want to talk about why I think the HP books and movies do so well. What J.K. Rowling does really well (and what the movie makers have translated well to the screen) is characterization.
Rowling's characters, human and nonhuman, all have depth. The good guys aren't perfect, and the bad guys aren't all the same. The white-haired Malfoys, for example, do care about each other, even if they don't seem capable of caring about anyone else. They're not so much evil as self-absorbed to an extreme degree. Snape embodies loyalty and will work toward a goal no matter what it takes to achieve it. Ron and Hermione become friends first, and sweethearts second. One reason they take so long to realize they're more than friends is that they're both afraid of rejection and the loss of that friendship.
Harry himself is often tempted from the path of doing what's needed by his own desire for a safe, secure place in the world. Some writers fear the idea of writing in a series because they think it limits them, but Rowling's work illustrates that it also allows the writer to develop the characters more than can be done in one book.
And of course, it doesn't hurt that a fantasy world is not limited by reality. Rowling can give Harry challenges no child in the real world would face. Setting the story in the familiar world of an English boarding school was a stroke of genius because it gave the characters' lives a recognizable framework that made the fantastical elements all the more magical.
Another reason the books and movies are so big is they appeal to both kids and adults. One reason children's classics stay in print for so long is, parents tend to buy the books they loved for their own kids, once they have them. This suggests HP will be big for generations to come. There is now a Wizarding World of Harry Potter in Florida (my boss went there for his 55th birthday!) that lets the reader/movie goer experience an approximation of Hogwarts. I suspect the movies, the books, the theme park, and the fan fic will all feed each other and make Harry Potter a big deal for a long, long time.