Hilary was a 12-year-old girl with a severe heart condition.
Tessa tells Dean that, because he is Death for the day, he has to kill her. Dean refuses, and her heart miraculously heals. This sets off a chain reaction in which a nurse, Jolene, dies before her time, and her husband, Scott, consequently drinks and drives. Scott almost crashes into a busload of people, but the accident is averted at the last minute when Dean takes off Death's ring and jerks the wheel of Scott's car. Dean saved his and countless other lives, but because he took off the ring he lost his wager with Death.
Tessa tells him that it's over, but Dean still goes back to the hospital and kills Hilary because he has learned his lesson: you can't mess with destiny or the "natural order."