If you are open-mouthed, your mouth has fallen wide open because you are very surprised or shocked. For a moment you are not thinking about your face; the feeling has done it for you. Writers like the picture: an open-mouthed crowd, open-mouthed amazement. People also stand open-mouthed at something huge or wonderful, so the feeling can be wonder, not only bad shock. You often put it before a noun, or after stand, stare, or watch. Though actually, sleeping with your mouth open is just a mouth position — that is not what this word is usually doing. Ordinary story-like English, not a science word.