Soldiers of the lowest rank in the military, or informal slang for someone's genitals.
From Latin 'privatus' meaning 'withdrawn from public life' or 'personal.' As a military term, it refers to soldiers with no special rank or authority—the most 'private' or lowest level of soldier.
The word 'private' originally meant something kept secret or away from the public, which is why both the lowest-ranking soldiers and personal body parts share the same name—they're both 'private' in the sense of being separate or excluded.
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