The frame material, binding plate, and highback all help to determine the flex of a binding. This flex is usually rated on a scale from 1-5. Aim for the comfort and forgiveness of a softer flex if you're a beginner or like a riding park, or the control and support of a stiffer binding if you're strong, experienced, or into riding steep, technical terrain.
Just like boots, bindings come in a variety of sizes. Often, bindings accommodate a range of boot sizes (example: s-m or m-l). It's important that you buy a binding in a size that matches your boot size. Similarly, if you have a board with 4-hole binding mounting pattern or the Burton Channel system, you need a binding that matches this mount type.
Other factors to consider in buying a binding include: adjustability of the highback angle and rotation, amount of cushioning underfoot, canting (angling) of footbed, and strap design. Most bindings feature the traditional two-strap style; a rear-entry step-in design that is easier to get into is also available from some brands.