To lower or remove your hat as a sign of respect or greeting, or to show respect by bowing.
From Old French 'valer' and Latin 'valere' (to be strong, to be worth). It originally meant to lower something as a sign of submission or respect, evolving from the physical gesture of removing one's hat.
Vailing—removing your hat to someone—was so important in medieval and Renaissance culture that it became the whole gesture of respect, and somewhere along the way 'veil' got confused with 'vail,' which is why we still say 'veil' today but 'vail' is the older, cooler word!
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