Neural oscillations are rhythmic or repetitive electrochemical activity in the brain and central nervous system. Such oscillations can be characterized by their frequency, amplitude and phase. Neural tissue can generate oscillatory activity driven by mechanisms within individual neurons, as well as by interactions between them. They may also adjust frequency to synchronize with the periodic vibration of external acoustic or visual stimuli.[3]
As a relatively new technology, fMRI has only recently been used to assess brain state changes during meditation. Recent studies have shown heightened activity in the anterior cingulate cortex, frontal cortex, and prefrontal cortex, specifically in the dorsal medial prefrontal area during Vipassana meditation.[7] Similarly, the cingulate cortex and frontal cortex areas were shown to have increased activity during Zen meditation.[8] Both studies comment on the possibility that these findings could indicate some state of heightened voluntary control over attention during mindfulness meditation. Review works by Cahn and Chiesa state that these results indicate consistency in meditation’s effect on these regions of the brain, citing a multitude of other studies spanning other meditative disciplines, but mention the need for further investigation with better controls.[4][6]
OK – so some of this is pretty common marketing hype. Consumers have become almost numb to such hyperbole. But still we see some of the common – almost ubiquitous – elements of pseudoscientific scams. The company claims that the device is “effort-free”, that the results are “rapid and long-lasting,” that it is the “most effective” method of its kind, and that it is useful for a broad range of applications (hey, why limit the market). I am used to such hype about dishwashing detergent, but find it intolerable when applied to a pseudoscientific device with medical applications.
Over-arousal in certain brain areas is linked with anxiety disorders, sleep problems, nightmares, hyper-vigilance, impulsive behaviour, anger/aggression, agitated depression, chronic nerve pain and spasticity. Under-arousal in certain brain areas leads to some types of depression, attention deficit, chronic pain and insomnia. A combination of under-arousal and over-arousal is seen in cases of anxiety, depression and ADHD. more...
Beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the third harmonic (i.e. second overtone) of the bass note beats with the second harmonic (first overtone) of the other note. As well as with out-of tune notes, this can also happen with some correctly tuned equal temperament intervals, because of the differences between them and the corresponding just intonation intervals: see Harmonic series (music)#Harmonics and tuning.
Your brain operates at certain levels of activity – the normal waking, active Beta, the meditative Alpha, the asleep-and-dreaming or deep meditative Theta, and the deep sleep/unconscious Delta. Beta is characterized by one thing we all want to get away from – stress.But that brainwave state has its place. It’s the action mode, and that’s the way it should be! If we’re not alert when we’re awake, bad things can happen, right?
Binaural beats are the playing of two sine waves of close, but not the same, frequency into different earpieces of a set of headphones. The "beat" is heard as the brain tries to process them as a distinct sound, while taking into account the constructive/destructive interference. It is said to migrate brain waves to be closer to that frequency, like a sort of biological resonance, which is true. Of course the same can be said for listening to relaxing music help you relax, up tempo music to help you feel energetic, etc...

You don't have to buy one, though. It's not too hard to make your own binaural beat, and free software is widely available to do just that. The one that I used to make that little sample is an open-source program called Gnaural, available on the Sourceforge website. It's pretty easy to use, though it takes some practice before you can generate some of the really cool, more professional sounding beats. A binaural beat consists of two simple tones, and most people add that background pink noise. Nothing special.