Stiff-necked describes a person who is too proud to listen, change their mind, or do as they are told. It is an adjective, always written with a hyphen, and it is used before a noun ("a stiff-necked old man") or after be ("they were stiff-necked"). The picture inside it is a neck that will not bend — you cannot bow your head, so you cannot show respect or admit you were wrong. It is a criticism, and a fairly heavy, formal, old-sounding one. You meet it most in religious language, in history writing, and in serious speeches; in ordinary conversation people say stubborn, pig-headed, or arrogant instead. The religious flavour is not an accident: the phrase came into English from the Bible, where a whole people is called stiff-necked for refusing to obey God, so the word still carries a note of moral judgement — not just "won't change" but "wrongly won't change." Note that it is not about the body. If your neck actually hurts, you say "I have a stiff neck" (two words, no hyphen), which is a completely different, everyday thing.