The phrase "flat sheet" refers to a rectangular piece of fabric that is typically used to cover a mattress. It is not fitted or elasticized and is usually tucked under the mattress to provide a smooth surface for sleeping. Full definition
Our Hotel Flat Sheet in classic white is nothing short of a bedtime essential. (gaylordhotelsstore.com)
Together with flat sheet of cloth diaper and waterproof baby mattress, it was how people raised babies 30 years ago in the third world country. (babycenter.com)