As you move through the brain states you create a certain frequency of brain wave patterns that can be read by the device and interpreted. Although the toy manufacturers simplify this by stating you just need to do two simple things- concentrate or relax, there are many more levels between and that's where you can create some real magic. It's like a video game. One person with lots of skills can do things in the game an inexperienced player would think was magical- but it's just focus and control.
The trick is to maintain a specific frequency by controlling your emotions and thoughts. As you think your brain responds to how you feel, loosely put, your emotions are a byproduct of your thoughts and cause the brain to release chemicals. These chemicals become emotions incarnate (to put it succinctly). The whole thing causes your brainwaves to fluctuate.
For example, when you're angry your in one frequency (tense/concentrated), and when your happy your in another (relaxed). This is an extreme set of cases as the fluctuations are often highly varied, but when you focus on something you can create a sort of macro that triggers an emotion.
Think of how you feel when you see a picture of someone you like and how you feel when you see a picture of someone you don't like. The feelings, unless something changes in the associations created with those people, tend to be the same or in the same ballpark.
Your thoughts generally cause your brainwave patterns to fluctuate widely and instantly but if you can figure out what thoughts cause you to feel certain ways you can essentially cause yourself to stay in a certain state. These biofeedback toys are great for teaching yourself to focus, meditate, and move a ball without touching it or anything (but wireless airwaves) that's touching it. As you saw in the "shocking" video above, someone can hack this device into a torture device (or is it learning to relax so you don't get shocked, device?).
It's not easy to maintain focus to the point where you can control the ball at first but in time you become expert. The kid in the previous video seems to be able to float the ball and drop it with relative ease. I'm thinking that this has to make some kind of changes in your brain and evolve the way you think so I think it has mental health/focus benefits.