If you drape a piece of cloth somewhere, you place it there so that it hangs down in a casual and graceful way.

If someone or something is draped in a piece of cloth, they are loosely covered by it.

If you drape a part of your body somewhere, you lay it there in a relaxed and graceful way.

Drapes are pieces of heavy fabric that you hang from the top of a window and can close to keep the light out or stop people looking in.