There are different kinds of clasps on a bracelet. For example:
Hooks: Oldest type of clasp available. It has a simple hook on one end and a hole in the other. Hooks are of many shapes and patterns.
Magnetic Clasps: Magnets at both ends of the bracelet.
Button toggle Clasps: This has matching buttons on both ends, one with a loop that is looped around the other.
Lobster Clasps: There are many shapes in lobster clasps. The main idea is to have a spring-loaded clasp on the one end that opens up slightly to facilitate to hooking it on the ring at the other end.