If you do something half-heartedly, you do it without much effort and without much interest in the result. The -ly turns the idea into a way of doing: they clapped half-heartedly, he studied half-heartedly, she smiled half-heartedly. It has the same slightly critical tone as half-hearted. Though actually, in real speech people sometimes just say they “weren't really trying” and skip this longer word. You will still meet it in stories and in complaints from teachers and coaches.