An open-necked shirt is worn with the top button undone, so the collar does not close up around the neck. It looks more relaxed than a shirt done all the way up, especially without a tie. You hear it most about men’s shirts, and about how someone is dressed for a warm day or a less formal office: “He wore an open-necked white shirt.” Though actually, it does not mean the shirt has no collar, and it is not a V-neck jumper — it is about that top button (sometimes the next one too) left open. British English uses this compound a lot; it is a clothes word, not a word about the body itself.