mid-14c., "costly silken fabric of one color having a repeated pattern of the same color woven into it," from Old French diapre, 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 "thoroughly" (see dia-) + aspros "white."
Aspros originally meant "rough," and was applied to the raised parts of coins (among other things), and thus it was used in Byzantine Greek to mean "silver coin," from which the bright, shiny qualities made it an adjective for whiteness.
The sense of the English word descended through "textile fabric having a pattern not strongly defined and repeated at short intervals," especially, since 15c., of linen where the pattern is indicated only by the direction of the thread, the whole being white or in the unbleached natural color.
By 1590s this led to a sense "towel, napkin or cloth of diaper;" the main modern sense of "square piece of cloth for swaddling the bottoms of babies" is by 1837 and became common in 20c. Also "any pattern constantly repeated over a relatively large surface" (by 1851).