It’s a cloth to cover over the futon for the prevention of contamination when you dry it in the sun. The nylon or polyester synthetic fiber sheets are widely used.  The sheet to lay under the futon is to prevent it from touching the dirty handrails of veranda or windows and the sheet to cover over the futon is to protect it from the dirty air such as car exhaust or bird dropping. There is also the sheet designed to prevent the futon from getting tanned or to make the futon dry easily by absorbing the sunlight effectively.