A curb bit is made up of several parts. The ported mouthpiece works on the horse's tongue, and the roof of his mouth. The shanks (the pieces that come down from the mouthpiece) are used for leverage. Some curb bits have a ring right by the mouthpiece, and require two sets of reins. The curb chain- a chain or strap that goes under the horse's chin from the top rings of the bit- add additional pressure under the horse's chin.
There are infinitely many specific styles and designs of curb bits.