An armhole is the opening in a shirt, dress, jacket, or other piece of clothing that you put your arm through. The sleeve is sewn around it; on a sleeveless top, the armhole is the open edge you see. People who sew and people who sell clothes use the word a lot. In a shop you might just say “this bit is tight under the arm.” It is a plain compound: arm + hole. Though actually, it is a hole in the clothes, never a hole in your body. If a jacket is tight at the armhole, lifting your arm feels stiff. Older English sometimes wrote it as two words, arm hole; today it is usually one word.