What does it mean when they say it is the mark of the cultured man that he is aware of the fact that equality is an ethical and not a biological principle?

It simply means that a reflective individual understands that each human being is born with traits and abilities which he inherits from his progenitors. Some of these abilities are more valued by the group as a whole and this gives that individual a "leg up" in a society. We know these tenets to be true.

But, to a cultured person each individual who is born has the right to be assessed as an equal in that society as a matter of fairness. Thus, we understand that it is an ethical principle that we, as a group, aspire to although we know that biologically this is not the case.