The flat sheet, also called the top sheet, originally is placed between the sleeper and the blanket. Its function is to make your bedding more welcoming. It also protects the blanket or the comforter from getting dirty. On warmer nights the flat sheet can be used by itself to cover the sleeper instead of a blanket.
The exact size of a flat sheet when purchasing is less important as it is used separately. One can use a queen size flat sheet on a double bed or vice versa.