Your knuckles are the joints in your fingers that are farthest from your fingernails. When you clench your hand into a fist, your knuckles are especially prominent.
A knuckle is the part of your hand that makes it possible to move a finger freely, and if someone offers you a "knuckle sandwich," you should politely decline, since they're actually planning to make a fist and punch you in the mouth. To knuckle is to rub with the knuckles, like when you knuckle a bit of sand out of your eye. The root of knuckle is the Proto-Germanic knuk-, "bone."