A clutch is a small finding that slides onto the post of an earring in order to secure the earring to the earlobe. They can be held in place by friction (friction back) or twisted onto a threaded post (sometimes referred to as a nut.) The friction style of clutch is typically composed of a disk with a hole for the post to pass through and two loops to provide the pressure on the post.
Earring with Clutch Backing.
Threaded Post and Clutch on a Stud Earring.