According to
Wikipedia:
"Cozy mysteries, also referred to simply as "cozies," are a subgenre of crime fiction in which sex and violence are downplayed or treated humorously, and the crime and detection take place in a small, socially intimate community. The term was first coined in the late 20th century when various writers produced work in an attempt to re-create the Golden Age of Detective Fiction.
..."
A good example would be the old Murder She Wrote television show.