Highness is the polite word you use when you speak to or about a royal person such as a prince or a princess. You almost never say it on its own. To their face you say Your Highness; when you talk about them you say His Highness or Her Highness (and Their Highness for more than one). It is palace language: very polite, rather stiff, and not for the street. You do not use it for a president, a boss, or a teacher — those have other polite forms. It is high + -ness, “the state of being high.” English also copied this way of naming a royal person from the same idea in Italian altezza, itself from Latin built on a word for high. Friends may say “Yes, Your Highness” as a joke when someone is acting too grand; that is play, not real court talk.