There are many ways to perform box jumps and they each have a different effect on your training. Mentioned here are single response (1 at a time) and multiple response (several in a row).
Single response: in a single response box jump, start standing on the floor and simply jump on top of the box with a soft landing, then step down and repeat. Use a good, powerful arm swing and choose a box height that you are confident with. This type of box jump improves speed and power. Use single response box jumps to help with dynamic exercises, like standing up during a heavy squat.
Multiple response: the goal of a multiple response box jump is to spend as little time on the floor as possible in between jumps. You can stand on the box as long as you’d like, just get off the floor quickly. Using a shorter box is better for these jumps (3”-12”). Multiple response box jumps work your stretch reflex to help with quickness during explosive exercises like sprinting.