A backless sofa is called a divan. This type of sofa is often situated against a wall where pillows can be propped up for more support.
Some divans feature an arm that angles upward on one end to support the head of someone who lies on the couch. This particular style of divan is called a fainting couch, and it is associated with the Romantic period of the early 1800s. Divans originated in the Middle East, where mattresses were pushed up against a wall for additional seating in public buildings called divans or diwans. Divan sofas made their first appearance in English society in the early 1700s.