A damask cover is a quilt or blanket that has a pattern of small, repeated designs. These small designs are usually made from blocks of color. A damask cover can be made from many different types of fabric, such as cotton, satin and silk.The patterns on the damask covers can be simple or elaborate. The patterns can be made up of one color or a variety of colors.The name “damask” comes from the city of Damascus in Syria. The first damasks were woven in this city.