You see people doing box jumps for a variety of reasons. In an athletic setting they are done as a power production exercise; in a CrossFit gym they are often done in a metabolic conditioning circuit; in commercial gyms they are done for...well, who knows why.
Why are YOU doing box jumps? The intent of the exercise is really as a power-production exercise. You're creating a situation where the athlete can jump as explosively as possible without having to worry about the stress from the landing. The eccentric portion of any exercise is where all the stress lays; so if we can take that out the athlete can perform that exercise with greater volume and intensity. It's also a great way to get athletes doing something athletic early in their pre-season programs.
Let's go over proper and improper form, as well as some useful variations.
The goal of the box jump is not to jump on the highest box that you can physically get on to. If you watch someone do a super-high box jump, all they are really doing is expressing their hip mobility. Sure, they still have some boost; but watch their hips as they get to the box. They end up with their knees up by their ears: not an athletic position.
Sure, it's impressive. I mean, I don't know if I can do that. But it's not a box jump. His knees come way up and he can't even control his landing. Plus, he took an approach which turns it into a different exercise.
A proper box jump should begin and end in the athletic position. Your goal is to jump as high as you can and just land on the box. Be explosive and think about trying to jump over the box, not just onto it. Also, make sure you step down off of the box for every rep. The box is there to allow you to avoid the eccentric stress of a jump; jumping off the box after a rep negates the point of the exercise. The eccentric portion can be explored with other exercises at the right point in the cycle.
Once an athlete gets really explosive, there are other variations to try rather than just using a higher box. That just allows the athlete to express how high he can jump, rather than making the exercise harder. For your first variation, let's take away the countermovement to the jump. For the concentric-only box jump, start off by sitting on a shorter object (a low box, some plates or even a dynamax ball).
Using a weight vest will allow the athlete to move with their normal mechanics, but they will be jumping with an added number of pounds.
Providing the athlete with (light) dumbbells to hold with alter their mechanics by not letting them use their arms to swing into the jump, but they will still be able to get the countermovement from their legs. This is an awkward movement for a lot of athletes so make sure you start with a lower box.
The last variation I'll go over is the 180-degree box jump. This particular variant is a good way to help improve proprioception in an athlete while simultaneously de-loading them. (Because of the awkward nature of the exercise, you'll use a lower box and probably won't need to add any external resistance).
I hope you enjoyed the post. I'll soon be going over more ways you can help improve your athleticism. Have a great day and go lift something heavy!