The Naked Apron is a fetish cosplay. The wearer will either be in underwear or naked with an apron covering their front.
American soldiers during World War II often had pin-up of naked women only covered in the front by aprons as part of soft-core "Peek-A-Boo" shots, this spread to the Japanese culture just as the manga culture was beginning in the 1945-60's. The design of the naked apron is based on the theme of domestic sexuality. It's involves a level of modesty, seduction, and submissiveness. The idea of a woman subtly seducing her lover by surprising him that behind the apron she isn't wearing anything.
Naked Aprons are used mostly as fan service and occasionally for comedic effect, largely depending on the nature of the series. Many consider the naked apron to be a fetish.
Often worn by maids, in anime and manga, the wearer doesn't strictly need to be completely naked under the apron for it to count as a naked apron. The apron is in some cases worn with underwear or skimpy swimwear like a bikini underneath.
A naked apron is considered particularly effective when the wearer acts as if nothing is out of the ordinary, especially if they're typically a shy person, like in the first notable example listed below.