"process of making mats," 1720, from mat (n.1). Meaning "fabric of coarse material for mats" is from 1748.
mid-13c., "Damascus;" late 14c., Damaske, "costly textile fabric woven in elaborate patterns," literally "cloth from Damascus," the Syrian city noted for fabric; see Damascus. From c. 1600 as "a pink color," a reference to the Damask rose, which is native to that region. As an adjective, "woven with figures," 1640s. Related: Damasked.
"pattern of squares in alternating colors," c. 1400, short for checker (n.1). As a fabric having such a pattern from 1610s.
type of fine fabric for ladies' dresses, 1840, of unknown origin, perhaps from the surname. Said to have been first manufactured at Norwich c. 1832.