More than any other component, bindings distinguish the performance of one brand of shoe from the next. The lace starts at the toe and zigzags back and forth toward your ankle. They're a cinch to operate while wearing mittens or gloves. They're widely adjustable and will work with light or heavy hiking boots, as well as insulated pack boots. These use nylon webbing and molded plastic buckles, just like the ones on your backpack.
Buckle bindings are lightweight and inexpensive.
Buckles sometimes jam with snow, making them difficult to adjust. Buckles tend to loosen as you walk, and require regular tightening. In extreme cold, plastic buckles have been known to crack. Ratchet bindings buckle across the toe and behind the heel. Rigid structure doesn't necessarily conform to small feet.