The drape of fabric or material is the way it looks — the shape it takes — when it's hanging. If you're sewing a dress, you need to use fabric with the right sort of drape.
You can describe the drape of a piece of velvet or cotton — and you can also use drape to mean "curtain." You could even say, "I just love the drape of those drapes!" When drape is a verb, it means "to cover loosely," as when you drape a quilt over your old sofa to hide its the rips and stains. In the 1940s and 50s, drape was also a slang term for a cool suit of clothes.