A he-rem is a harem of dudes that an attractive woman gathers around her by rationing sexual favors. A common tactic is to be interested in a guy, sleep with him such that he is really interested in her, then say "let's just be friends". If he agrees to this he becomes a member of her he-rem. He will do things for her and give her attention when she requires it, without receiving any sex.
I refuse to join her he-rem. I still have some self-respect.