This sleep restraint was used in the Command Module "Columbia" on the Apollo 11 mission, the first to land humans on the Moon. During sleep periods, the restraints were placed under the left and right couches and on top of the right couch. They could be rolled and stowed behind the couches in the Upper Equipment Bay when not in use. The lightweight fabric with zippered front is meant to hold the astronaut from floating around the cabin in the zero-gravity environment of space. Straps on the back of the under seat sleep restraints (this is one of those) were used to attach to the inside of the cabin.
NASA transferred this sleep restraint to the Smithsonian Institution in 1972.