Make Mine a Mystery: Reader's Guide to Mystery and Detective Fiction by Gary Warren Niebuhr (2003) defines a cozy this way:
"In a cozy (or soft-boiled) novel the action is low on the description of violence, with little overt sexual content or abusive language. A soft-boiled world is one in which society is viewed as orderly and controlled, and the crime is a failure of the society to function correctly. The society portrayed is often a closed or confined set. The inclusion of a mystery in a soft-boiled world is an intrusion. Most violent action takes place off-stage. The emphasis is on the solution of the crime. Readers anticipate a world where right and wrong are clearly defined. The society depicted in a soft-boiled novel is more moral than in a hard-boiled world, and the reader expects the detective to follow clues left by the perpetrator to an eventual administration of justice. The detective is often an amateur, although not limited to this type of detective."
Agatha Christie's Jane Marple books are a classic example of the cozy. The Agatha Raisin books and the Booktown Mysteries are also cozies. Other examples include the Cat Who... books, the Phryne Fisher novels (though they are a bit racy for the classification) and most of the crime novels where a caterer (or a quilter, weaver, herbalist, home renovator, knitter, etc.) gets mixed up in a criminal investigation.
There is a website dedicated to listing and classifying these books at http://www.cozy-mystery.com/