This is a relatively new term to describe a mystery story that has a focus on deduction and character development as opposed to blood and guts. Perhaps I exaggerate. But people who read cozy mysteries, much as they enjoy suspense, prefer that the murder take place off-camera. The perpetrator is no hideous serial killer with unnatural appetites. Instead he or he lives next door or works down the hall from you. The murder is 'out of character' and came about only because of a specific set of random occurring circumstances. The victim may be someone that few liked.
The reader follows the storyline through the eyes of the amateur sleuth whose innate talent and natural curiousity and intuition compel them to try to solve the crime. The clues are casually strewn yet at the conclusion it should be possible to trace back the hints and innuendos to the inevitable conclusion.
It goes without saying that it is totally unfair for the writer to make a transitory character, one makes a brief and unmemorable appearance, as the murderer. No, in a cozy mystery there must be several potential suspects each with the requisite motive and opportunity. Television programs, with their budgetary constraints have been known to skimp on this, to their detriment. After you discount the regular cast members, it quickly becomes apparent that the new arrival to town is the guilty party.
I prefer to read . . . and write . . . cozy mysteries. I could blame my weak stomach and that's certainly true for the movies and televisions shows I pass on due to their graphic visuals. It also seems, at times, that graphic violence and cut action sequences are substituted for storyline and character development. That rarely ends well.