I could go into a long monologue here about the transvaluation of values and how the higher man is uniquely suited to eventually create the Ubermensch through his down-going and so on, but I think it would actually be more productive to look at this from the angle of Nietzsche’s amor fati because that’s how it plays out in an individual life. You have to remember that Nietzsche was, in large part, a social philosopher. He wanted to give a diagnosis for the present state of civilization, figure out why it is the way it is, and use all those findings to make a prediction for where it’s going. I’m purposefully avoiding a characterization of the higher man in that way (i.e. the social perspective) because I’ve already covered it numerous times here on Quora. I want, instead, to look at how it plays out for individuals.
So Nietzsche has this idea of amor fati or “love of fate,” which is that you affirm the conditions of your life and being. That, in turn, is a fancy way of saying that you radically accept the way your life is and what you are. You can try to change your circumstances, of course, and no self-respecting higher man would be satisfied with going through life without actualizing his potency and furthering his Will to Power. But love of fate is a way of avoiding resentment. Nietzsche sees slave morality — as another answer notes, this may be better thought of as slave mentality — as a kind of resentment, not only in the form of envy towards those who have more than you or are better than you in some way, but resentment toward life itself. If you find yourself looking at the cosmic unfairness of it all and decide that you hate existence, that you’re a Schopenhauer-esque pessimist who sees the world as a bad place and must deny it, then you have become resentful of everything, life and yourself included, and your entire psychological structure, your whole being, is corrupted with resentment. This is slave morality: a spiteful lashing-out against the universe itself for creating you as an inferior being that loves to lash out at the universe for not giving it what it wants. If that sounds like a big circle, it is.
The higher man, however, either never had a problem with being who he was, or has, through some faculty or quality present in him from the beginning (Nietzsche did not believe in free will) managed to jettison his resentment and simply affirm himself and the world he lives in. This means that the higher man literally has no shame or guilt, except where he himself judges that his actions have been wrong. You can punish the higher man and call him anything you want, you can even kill him, but you cannot judge him, because the higher man is “morally” beholden only to his own judgment. The higher man has no resentment, and his absence of resentment is the surface-level effect of a unified will, instincts acting in concord because there is no existential fracture in him as there is in the slave. Those in the grip of slave morality rail against existence for making them spiritually deformed; the higher man does not even have time to give his disdain to the slaves. He’s too busy creating.
This is where a lot of people, particularly people who feel slighted by the world, tend to get very angry. They’ll accuse Nietzsche, and anyone propounding (or merely explaining) his philosophy, of some kind of fascism or bigotry or malignant self-satisfaction. If you constantly feel as if you’re surrounded by stuck-up bastards who think they’re better than you, and if you’re convinced that the world gave you a raw deal, these ideas may irritate you. Not that Friedrich would care — he’d just smirk beneath that magnificent mustache.