Girl breaks up with guy, but not for first time (guy was cheating?). Girl gets over guy quickly, goes out with other guys, but first guy realizes he's erred and can't get over her. Guy wants to get back together, or at least talk and get closure. "See me in your eyes" has two meanings - the guy wants to hear what the girl thinks of him and what kind of person he appears to be. The second meaning is literal - he wants to look into the girl's eyes with sincerity and see his reflection in them.
Girl breaks up with guy, but not for first time (guy was cheating?). Girl gets over guy quickly, goes out with other guys, but first guy realizes he's erred and can't get over her. Guy wants to get back together, or at least talk and get closure. "See me in your eyes" has two meanings - the guy wants to hear what the girl thinks of him and what kind of person he appears to be. The second meaning is literal - he wants to look into the girl's eyes with sincerity and see his reflection in them.