Damask is a luxurious, heavy fabric that's often used to upholster furniture. Your grandparents love their new kitten so much that they don't even mind her clawing holes in their damask curtains.
The word damask comes from Damascus, the Syrian city where this kind of fabric was originally made — it literally means "cloth from Damascus." Damask was one of the main styles of weaving during the early Middle Ages, and it has been a popular choice for fancy clothing, table coverings, and home decor ever since. Today some damask is made of synthetic material, but historically it was most often made from silk.