When a heterosexual man has intense admiration for another man, to the point that it seems like sexual attraction (but it's not). This is usually a submissive-dominant relationship, since the person with the man crush will usually do or say anything to win the respect of (or a high-five from) the crushee.
Person 1: Jay's not here, he's off playing one-on-one basketball with Frank.
Person 2: I thought Jay hated sports
Person 1: Man crush...
Person 2: Ah, say no more.