Theresa was Boone's childhood nanny. Boone loved to torment her by calling her up the stairs all day. One day, when Boone was 6, she fell down the stairs and broke her neck. Boone felt responsible for this. It is not known whether the fall killed her. ("Deus Ex Machina")
In a dream, Locke saw Boone repeating, "Theresa falls up the stairs, Theresa falls down the stairs," before Boone told him this story. This revelation led Boone to believe Locke's dream was more than just a dream.