Professor Binns is Hogwarts's only ghost teacher. He doesn't appear to have noticed that he has died; he's just continuing on in his routine of teaching History of Magic as though he were alive. Professor Binns's class is hugely boring (in part because he doesn't know any of the students' names and doesn't ask or answer questions).
One day, though, Hermione goes ahead and asks Professor Binns to explain the legend of the Chamber of Secrets. It takes some persuasion, but he finally tells his class about a feud between the four founders of Hogwarts, Godric Gryffindor, Rowena Ravenclaw, Helga Hufflepuff, and Salazar Slytherin. Slytherin wanted to keep Hogwarts for purebloods, while the other three were willing to accept talented Muggle-borns. Finally, Slytherin left the school over this issue of blood. However, so the story goes, Slytherin left something behind: a secret chamber that contains a monster. Only a direct heir of Slytherin could open the chamber and unleash the monster inside.
After explaining this fascinating story, Professor Binns returns to his curriculum, "and within five minutes, the class had sunk back into its usual torpor" (9.117).