Magic was real, and hidden away from the world. People with magic attended normal schools and had normal lives, but trained in magic and learned magical history and things like that on the side, and there were hidden areas of cities -- and even some entire small towns -- for mage-sorts only. There were two main factions in the dream; the Guardians and the Hidden. The Hidden thought that magic should be used to dominate those who didn't have it and weren't aware of its existence, while the Guardians felt magic should be used in a protective way.
J.K. Rowling was one of the Guardians; she wrote the Harry Potter books as a way of fictionally retelling the conflict between the two, in order to prepare people for learning the existence of magic, and make them a little less prone to falling for Hidden tricks. The Hidden didn't like this, and so they stirred up the various campaigns like the fundamentalist Christian group who say that Harry Potter books turn people to the path of Satan.
Some of the HP characters were based on actual people in that conflict; a high-ranking Hidden, Lucas LeRoi, and his son David LeRoi were the models for Lucius Malfoy and Draco Malfoy. I think, though I'm not sure since a lot of the dream is blurry in retrospect, that my dream-self (I wasn't /quite/ myself, though personality-wise I was similar) was the basis of Hermione. I think my name in the dream was Heather.
I don't remember most of the dream, except that my dream-self was arguing with David LeRoi at Disney World(?) and we were getting to the point of brandishing wands at each other. Then I woke up...perhaps thankfully.