"The Baby" is the nickname that Stoyte gives to his young mistress Virginia Maunciple. Stoyte discovered Virginia when she was working as a chorus-girl in a night-club. In that sense, he looks upon her as a kind of trophy girlfriend, someone he can show off to the world as a sign that he's still virile and strong despite his advancing years. As we soon discover, Stoyte wants to live forever. He's a self-made millionaire, with all the trappings of wealth and success—including a sexy young mistress—but the one thing he can't buy with all his money is immortality. At least not yet.
As well as being a mistress, Virginia's like the daughter that Stoyte never had. Hence her nickname. Yet when Stoyte calls Virginia his baby, he doesn't just mean it figuratively, but literally. This seriously complicates his feelings towards her—a toxic, unstable mixture of "the purest father-love and the most violent eroticism."