A hard-on is a very informal, rude word for when a man's penis is stiff because he is sexually excited — an erection. Doctors and school books say erection. This word lives in jokes, films, locker rooms, and private talk among friends, not in class, emails, or a doctor's room. Students often meet it in songs and subtitles long before they need it, and they do not need it to be polite. It names a male body fact; it is not a careful or medical term. Though actually, a different phrase looks almost the same and tricks people all the time: to be hard on someone means to treat them strictly, with no sexual meaning at all. The little line in the middle, and the a (a hard-on), mark the slang noun.