Harry is going to be the new Hogwarts Defense Against the Dark Arts professor. He needed a change from the way his life had been going. Unfortunately, he finds out Draco Malfoy is also going to be starting as a Hogwarts professor. Their rivalry is, of course, not budging. But since they're teachers now, they're not allowed to fight (well, they tried, but going against Minerva McGonagall's wishes is never advised). They both become fixated on proving they're the best teacher: who's most popular with the students, who has the best teaching methods, who gets the most compliments and gifts before breaks. Everything. As a result they are always lurking around each other's classes, eager to brag that they've got a one-up.
Their students start to get a slightly different impression about their relationship than Harry and Draco have.