a fold on a bed sheet or blanket made by tucking the foot or head of the sheet straight under the mattress with the ends protruding and then making a diagonal fold at the side corner of the sheet and tucking this under to produce a triangular corner.
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British Dictionary definitions for hospital corner
a corner of a made-up bed in which the bedclothes have been neatly and securely folded, esp as in hospitals
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012