When we last left Harry, he had been forced to take part in the Tri-Wizard Tournament and witnessed the rebirth of Lord Voldemort. Unfortunately, it doesn't look like this year at the school will be much easier.
Harry Potter and the Order of the Phoenix starts off with Harry being attacked by a pair of dementors outside of school. After his hearing for using magic in the presence of muggles, it becomes clear that the Ministry of Magic is refusing to hear that The Dark Lord has returned, and all that becomes even more obvious when classes start up.
With a new, Ministry-appointed Defense Against the Dark Arts teacher, Harry, Ron and Hermione decide that they aren't getting the quality of education they need to go up against the real-world issues they will all soon be facing. So they start up a secret club called Dumbledore's Army. Most of the game centers around scavenger hunt missions designed to convince fellow students to join the DA. There are a few duels scattered throughout the story, as well as the eventual hunt for whatever his hidden at the Ministry that Harry keeps dreaming about.
The game takes place in two locations: Hogwarts and Number 12 Grimmauld Place, though you'll eventually venture to the Ministry of Magic. With the exception of the Ministry, each location is a semi-open world in that you can roam around the place. You can go wherever you like, though a few areas are locked off until you find a password or a story segement happens. As you explore, you will earn Discovery Points. These points basically reward the player for interacting with objects and recognizing familiar elements from the game and movie.
As far as the exploration and discovery aspect of Order of the Phoenix, this is great for fans. Unfortunately, the gameplay aspects (the hunts and duels and mini-games) aren't all that interesting, at least not after the dozenth time you've done one.