These are the things that keep your boots
(and presumably your feet
) stuck to your snowboard
. They come in two main styles
The clip-ins are the kind you usually see in cheap rental snowboards. The advantage to them is that they are fast and easy. You basically just step onto your board, and your feet 'clip in'. There are several disadgantages to this type of binding, however. First of all, you have to have boots which fit into the bindings. You can't just step in with any boots.. the connector has to be there. Also, they don't offer as much support as the strap-ins. And they have a very annoying habit of getting full of ice. Once full of ice they don't work properly until you take off your gloves and force it out with your fingers, a very unpleasant maneuver.
The strap-ons take a bit longer to get into; they consist of some sort of strapping mechanism fastening your boot to the board. Although they are somewhat slow, they are usually supportive of your boot.. and you can use any good snowboarding boot as long as the binding is the right general size. They are adjustable for different angles, and they don't stop working when full of snow.
Since both feet are fastened to the board, you can't go anywhere other than down while strapped into the board. This is extremely annoying in ski-oriented runs where there are long flat areas; you have no poles to push out and can't 'walk' so you have to remove your back foot and push yourself along. This is also how you get on or off of a lift (its tricky to ride the board off the lift with only one foot strapped in, which is why you use a stomp pad sometimes. If you've got a long way to go, you just have to take off both straps and carry the board.