Used when someone physically shows they are worried or upset, usually not in formal situations. During the intense movie scene, we all started wringing our hands.
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Non-literal use
Sometimes used figuratively to describe someone who's extremely anxious but not actually twisting their hands. I've been wringing my hands over this decision for days.
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Sign of unease
It's a way to subtly indicate that a character in a story is nervous or fearful. He wrung his hands as he waited for her answer.