A "lazy" or deficient eye. When one eye will look where the person intends, but the other is staring off in some other direction. Particularly unnerving for anyone trying to talk to a person with a "broken eye" as they can't tell where the other person is looking.
"Some guy at the bar started talking to me last night during happy hour. I don't even remember he was talking about, cause I distracted by his broken eye. He was looking at me and the wall on the other side of the room at the same time."