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The "under" part is clear enough, but what about "drawers"?
That word refers not to where you store them (i.e., in a chest of drawers), but how you put them on.
The word drawers has been used since the 16th century to refer to garments such as stockings, underpants, and pants. It comes from the verb draw used in the sense of pull, probably because you pull them up your legs.