SKI BINDINGS
Bindings are the devices that hold your boots onto the ski. They are designed so that if you get into trouble, your boot should detatch from the ski, before you can hurt your legs.
DIN Settings
The most important thing to know about bindings is DIN settings. This is the tension adjustment on the front and back parts of the bindings, and it determines how easily your boot will be released. What these should be set to is calculated by your weight, height and ability, and are best to be set in the shop you get your skis from. A lot of shops will even test to make sure the bindings release under the correct forces.
Ways a Binding will Release
A ski binding will release a ski boot in 2 different ways. The front of the binding lets the boot release if there is a large twisting force.

The back of the binding lets the boot release if there is a large forward force on the boot. On some bindings the back will also release with twisting forces.

Brakes
Ski bindings also have brakes, these are the 2 arms that stick into the snow when there is no boot in the binding. They stop your skis flying away when you take your skis off, and help keep your skis in the right position as you put them on.
The information here is for an alpine skiing binding. Bindings for other types of skiing can be quite different.
Move on the the Ski Boots section.