We don't ever learn what this creep is the boss of, but clearly he's some kind of big-shot. He's "jowly," "pot-bellied," and has "the fierce redness of an athlete forced into idleness" (8.8.1). He's rich, he's married, and he's mean as a snake. His apartment has been decorated to resemble a brothel, and his wife Natalie serves drinks wearing scarlet, skin-tight clothing and no underwear. On the whole, Boss is an unpleasant fellow in an unpleasant place.
Boss' reason for inviting Jael to do business is that he wants to propose an experiment. Sick of being forced to do women's work, Boss wants to negotiate a truce that'll bring the two sides back together. Once he gets talking about the glories of equality between women and men, Jael can't get a word in edgewise.
Boss is interested in making history and being a hero, not in improving the social conditions that led to the war in the first place. As though his ulterior motives weren't clear enough, Boss insists to Jael that once Manlanders and Womanlanders come back together, "m]ost women will continue to choose the conservative caretaking of childhood, the formation of beautiful human relationships, and the care and service of others. Servants. Of. The. Race" (8.8.34).
Boss meets a grisly end when he lets himself get too carried away with Jael. She gives him fair warning, but because he doesn't listen to a word that comes out of her mouth, it comes as a total shock when she finally shouts that she's going to kill him. Like the Host of the party on Riverside Drive, Boss tries to turn it around on Jael, and tells her that she led him on, it's all her fault, etc. Jael could walk away at this point, but she doesn't; instead, she lacerates him with her surgically-implanted claws and leaves him lying on the floor to bleed out.