I don't know who came up with this word to apply to a certain type of mystery. (Wait, I could probably google that and find out!). I've read different definitions on various author websites: they're the type of books you read in front of a fire with an afghan on your lap (the blanket, not the dog!) They're the type of book you take to the beach, they're a 'light' read. A website that features cozy mysteries, http://www.cozy-mystery.com/ describes the books as set in a small picturesque village or town with the kind of people you know as your neighbours--except for the murderer, once you know who he or she is. There is no gory violence and limited 'adult' situations. A few laughs along the way are enjoyable as well.
Everyone has different tastes and wants something different out of their reading experience. I think that applies to movies as well. I've found I don't like reading a book or seeing a movie that leaves me upset, traumatized or feeling guilty for being alive, healthy and happy. I realize it can be a terrible world, but much as I would like to, I cannot solve the world's problems. Other people have a different point of view. As others have said, it would be a boring world if we were all the same and liked the same things.
I think authors tend to write what they like. The genres I write in are interesting to me. I hope they will give readers an entertaining read and something to think about. But no nightmares.