The box jump is one of the simplest jumping exercises and is a good way to benefit from jumping while also being able to minimize impact.
Perform a standard countermovement jump up onto a box. It’s generally best to use a box well under what you can actually jump onto so you can focus on jumping as high as possible and coming down into the box slightly rather than having to strain to lift the feet to the box. Focus and demand on the legs can be increased by removing the swinging of the arms—hold the hands loosely at the chest. If needed to reduce impact, step down off the box and even use the arms to help assist.
The box jump is a basic exercise to develop explosive leg and hip extension.
Box jumps should generally be done for 3-5 reps per set, with 3-10 sets. In weightlifting, they are usually done at the end of a training session. This prevents their fatiguing the lifter for the performance of more sport-specific speed-dependent lifts, and also helps improve explosiveness by forcing the body to recruit more and higher-threshold motor units when partially fatigued.
Box jumps can be done without a countermovement, with a full squat countermovement or from the bottom of a squat, with one leg, to the side, from a seated position, and many more options.