There are two main reasons to get one of these. The first is if you want to strengthen your hand and arms. The second? To have fun!
First reason one. If you're looking for a way to strengthen your arm and hand, the powerball will definitely help you with this. Specifically, you have to hold on to it, so it works the gripping muscles of the hand. It also works the wrist muscles, because you have to rotate your wrist to keep the motion going. Lastly, your biceps will get a workout as well, because your biceps muscle helps turn your palm up (supination), which is one of the motions involved in keeping the gyro spinning.
I can't really see anyone with an acute wrist/elbow/arm injury using this device, as it would probably be just too vigorous a motion and flare things up. In other words, say you had really bad tennis elbow and could hardly grip things or move your wrist around much- I think the powerball would likely make it worse in the beginning. Maybe use it more later on as it got better as the powerball is definitely an advanced activity you could do to get fully back into shape. Exercises like those outlined in Treat Your Own Tennis Elbow
would probably work better than to jump into something vigorous like a powerball. Mild cases might do alright though.
On the other hand, if you don't have an injury and are just looking to get the above muscles stronger and in better shape, then the powerball will certainly benefit you. Because it can spin progressively faster and faster as you get stronger, the powerball can provide you with a progressive resistance of sorts to get you stronger and stronger over time.
Now the second reason to get a powerball, for fun, really needs little explanation- it's just too much fun seeing how fast you can get this thing spinning! Perhaps the only non-fun thing about it is that it does take a little practice to get the hang of it, and when you're starting out and can't keep it spinning, well, that can get a little frustrating. However, it doesn't take long, and one thing that helped me in the beginning was to keep my elbow straight as I was practicing getting the technique down.
All-in-all a cool toy and useful tool- don't think twice and give it a try!