When you say we "understand" what it's supposed to be, what do you mean? That morality is an attempt to generalize required behaviour over different situations was the point. The utility of the morality project is that has the goal of preventing any situation from going to hell. That's what makes the game compelling to participants. From a selfish game theory perspective, the repeated interactions is the argument for it.
Our common understanding of the concept of morality is something that is universal. We don't accept that there should be a different morality for the king vs. the peasant.