What does it mean if someone stares at you while singing?

If someone is singing professionally and looks at you it could simply be reaching out the audience and nothing else. If this is a person you know that sings well and looks at you, then it's possible they really do care for you. Entertainers are suppose to make their audience feel personalized to them (that's why you see bands ... especially the lead singer go around the edge of the stage either slapping people's hands or holding their hands.) Good PR!