A half-hearted action is one you do without putting your heart into it. You go through the moves, but you do not care much how it turns out. A half-hearted smile is thin. A half-hearted apology does not really mean sorry. A half-hearted try is weak, from boredom or from not wanting to be there. The word is a little critical: you are saying the person could have tried. Though actually, people also use it when someone is tired or unsure, not only when they are lazy. It usually describes an action, an effort, or support — a half-hearted cheer, half-hearted support — more naturally than a person as a whole. The opposite feeling is wholehearted: all in, fully meant.