Stirrups afford the rider greater stability and control of leg position. There are a number of styles available, depending on what kind of riding you do. English stirrups are made of steel and attach to the saddle with narrow leather straps, with holes to adjust the length. Western stirrups are thicker and wider than English stirrups, and are usually made of leather, but are sometimes made of wood.
The most important aspect of stirrups is that they fit properly, allowing your feet to slip out easily. Some stirrups have a modified design, while others have a rubber safety release. Rubber stirrup pads can improve your traction, but don't use them if you're wearing rubber-soled shoes, which may stick.
For most types of English riding, your stirrup leathers should be roughly the same length as your arm. To measure, place your fingertips at the top of the leather and stretch it out along your arm. The bottom of the stirrup should fit into your armpit. Jumping requires a somewhat shorter stirrup, while dressage riders use a longer one. Western stirrups are also longer, to allow for many hours in the saddle.