Ski width determines the width of the binding brake and mounting platform you need. A wide binding should be mounted to a wide ski, and a wide ski requires a wide brake. Most binding manufacturers offer a wide brake option, some of which go as wide as 130mm to accommodate powder or big mountain skis.
DIN refers to the release value of a binding. The DIN setting can be adjusted higher to help retain your foot in the event of a crash or lower to allow you to release more easily. Your weight and ability level determine the DIN setting you need. DIN can be as low as .5 and as high as 20+, although the specific range depends on the binding.
Some hybrid alpine bindings can be switched between a free-heel 'climb' mode and locked-heel 'ski' mode. This binding is a popular choice of skiers who want to ski in the backcountry and at the resort without having to own both a touring ski and binding and a resort ski and binding.Shop Alpine Touring Bindings