diaper (n.)
mid-14c., "fabric with a repeated pattern of figures," from Old French diaspre "ornamental cloth; flowered, patterned silk cloth," perhaps via Medieval Latin diasprum from Medieval Greek diaspros "thoroughly white," or perhaps "white interspersed with other colors," from dia- (see dia-) + aspros "white."

Aspros originally meant "rough," and was applied to the raised parts of coins (among other things), and thus was used in Byzantine Greek to mean "silver coin," from which the bright, shiny qualities made it an adjective for whiteness. Modern sense of "underpants for babies" is continuous since 1837, but such usage has been traced back to 1590s.
diaper (v.)
late 14c., "to put a small, repeated pattern on," from Old French diaprer, variant of diasprer, from diaspre (see diaper (n.)). Meaning "to put a diaper on" (a baby) is attested by 1951. Related: Diapered; diapering.