An adjective describing any fabric with or without a nap that has a very flat (as opposed to shiny or lustrous) appearance–due either to the weave or finish.
Not that matte fabrics are without life: a matte silk can be almost chalky in appearance, stonewashed fabrics are matte with subtle colour changes, and woven fabrics such as damasks are patterned with a matte ground and a silkier raised design that creates a light and shadow effect.