an argument etc that makes you feel certain that something is true or that you must do something about it:
Lucy had no compelling reason to go into town.
The court was presented with compelling evidence that she'd murdered her husband.
very interesting or exciting, so that you have to pay attention:
His life makes a compelling story.
a strong need, desire etc to do something, making you feel that you must do it:
He felt a compelling need to tell someone about his idea.