When signals of two different frequencies are presented, one to each ear, the brain detects phase differences between these signals. "Under natural circumstances a detected phase difference would provide directional information. The brain processes this anomalous information differently when these phase differences are heard with stereo headphones or speakers. A perceptual integration of the two signals takes place, producing the sensation of a third "beat" frequency. The difference between the signals waxes and wanes as the two different input frequencies mesh in and out of phase. As a result of these constantly increasing and decreasing differences, an amplitude-modulated standing wave -the binaural beat- is heard. The binaural beat is perceived as a fluctuating rhythm at the frequency of the difference between the two auditory inputs. Evidence suggests that the binaural beats are generated in the brainstem's superior olivary nucleus, the first site of contra-lateral integration in the auditory system (Oster, 1973). Studies also suggest that the frequency-following response originates from the inferior colliculus (Smith, Marsh, & Brown, 1975)" (Owens & Atwater, 1995). This activity is conducted to the cortex where it can be recorded by scalp electrodes.  
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...
In the 1980s, a researcher in Japan, Tsuyoshi Inouye described how light stimulation creates synchronization of brain hemispheres. Since then, other researchers have detailed the positive effects of hemispheric synchronization including a 1984 study by researcher Dr. Gene W. Brockopp stating that hemispheric synchronization resulted in improved intellectual functioning as well as improvements in long-term memory, and these effects are cumulative over time.
Women worry more than men do. A study of 166 married couples who kept stress diaries for six weeks found that women feel stress more frequently than men because women tend to worry in a more global way. Whereas a man might fret about something actual and specific—such as the fact that he's just been passed over for a promotion—a woman will tend to worry abstractly about her job, her weight, plus the well-being of every member of her extended family. Keep your anxiety focused on real, immediate issues, and tune out imagined ones or those over which you have zero control, and you'll automatically reduce stress overload.
Brainwave entrainment is a colloquialism for such 'neural entrainment', which is a term used to denote the way in which the aggregate frequency of oscillations produced by the synchronous electrical activity in ensembles of cortical neurons can adjust to synchronize with the periodic vibration of an external stimuli, such as a sustained acoustic frequency perceived as pitch, a regularly repeating pattern of intermittent sounds, perceived as rhythm, or of a regularly rhythmically intermittent flashing light.
As with meditation, mindful exercise requires being fully engaged in the present moment, €”paying attention to how your body feels right now, rather than your daily worries or concerns. In order to “€œturn off”€ your thoughts, focus on the sensations in your limbs and how your breathing complements your movement, instead of zoning out or staring at a TV as you exercise. If you’€™re walking or running, for example, focus on the sensation of your feet touching the ground, the rhythm of your breath, and the feeling of the wind against your face. If you are resistance training, focus on coordinating your breathing with your movements and pay attention to how your body feels as you raise and lower the weights. And when your mind wanders to other thoughts, gently return your focus to your breathing and movement.

When stress overwhelms your nervous system, your body is flooded with chemicals that prepare you for “fight or flight.” This stress response can be lifesaving in emergency situations where you need to act quickly. But when it’s constantly activated by the stresses of everyday life, it can wear your body down and take a toll on your emotional and physical health.
Deeper Meditation • Near The Stage Of Sleep • Vivid, Dreamlike Imagery • Creative Visualization • Feel More Open & Connected • Advanced Problem Solving • Super Creativity • Insight • Intuition • Inspiration • Deeper Subconscious To Super-Conscious Mind • Trance-like • GABA • Immune System • Serotonin • Endorphins • Acetylcholine • Lower Cortisol • Deeply Relaxed • Sleep Better • Emotional Intelligence

Most of these websites give some brief explanation of entrainment. The example you hear most often is that of Dutch polymath Christiaan Huygens, who in 1665, hung two pendulum clocks next to each other on a wall. He noticed that the pendulums eventually matched each others' frequency, but always in antiphase, opposite to each other, as if canceling each other out. He'd try disturbing one or setting them in sync, but they'd always return to the same antiphase synchronization. Huygen's experience is widely touted on binaural beat websites as a demonstration of how systems can become spiritually connected through some energy field. However, they misunderstand what happened, and have not read the full story. Huygens also tried taking one clock off the wall, and as soon as they were no longer physically connected to one another via the actual wall, the effect disappeared. It was not the proximity of the clocks to one another that created the entrainment; it was their physical, mechanical connection to one another. As each pendulum swung it imparted an infinitesimal equal and opposite reaction to the wall itself. With two clocks on the wall, the system naturally sought the lowest energy level, according to the laws of thermodynamics; and both pendulums would thus swing exactly counter to each other, minimizing the system's total energy.
Transparent Corp's Research Area is arguably the most comprehensive resource for collated brainwave entrainment research.   Update: the main research area on Transparent Corp's website is currently being updated, so it is offline.  However, you can still access their peer-reviewed research paper as a PDF here: “A Comprehensive Review of the Psychological Effects of Brainwave Entrainment“.
Some studies have found that binaural beats can affect cognitive function positively or negatively, depending on the specific frequency that’s generated. For example, a study of long-term memory found that beta-frequency binaural beats improved memory, while theta-frequency binaural beats interfered with memory. This is something for scientists to continue to examine closely. For people who use binaural beats, it’s important to understand that different frequencies will produce different effects.
Stress: We all deal with it, yet we know how much better off we’d be — both physically and mentally — if we could only get it under control and find stress relievers that really work. While stress can be a positive, motivating factor at times (such as when you’re under pressure to perform well at work or to ace an important exam), more and more research shows that chronic stress impacts the body in ways similar to a poor diet, lack of sleep or sedentary lifestyle.

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.
By the 1980s, entrainment technology had merged with advancements in microelectronics technology, making it possible to develop even more sophisticated audio and visual brainwave entrainment products for the marketplace. In the last two decades, a number of scientific studies have reported brainwave entrainment as an effective remedy for ADD, academic learning problems, and improving memory and cognition.
Brainwave entrainment is a simple concept. It’s simply causing your brainwave frequency to align with some intended frequency in order to produce some intended result. It’s a way of modulating your brainwaves to resonate at a certain frequency. Being that there are certain dominant frequencies associated with different states of consciousness, this is being researched as a quick and effective way to induce states such as sleep, alertness, concentration, and even meditative and deep sleep states.

The Delta brainwave is experienced by us every night in dreamless sleep. It is also experienced by advanced yogis and monks who can enter the Delta frequency during deep meditation. This frequency assists in both emotional and physical healing, as well as enhanced immune functioning, significant stress reduction, and even anti-aging benefits. The Delta frequency is a terrific way to experience deep repair on the physical, emotional, and psychological levels.

Effects on cortisol: The hormone cortisol is commonly associated with stress, and when levels are higher than usual, it can have a negative impact on the body. High levels of cortisol can lead to a range of conditions, including Cushing syndrome, menstrual cycle and female libido changes, anxiety, and depression. Dr. Giampapa noted a reduction of cortisol of up to 70-80 percent in several study participants.
You won’t recall ever being in this state, but it’s an incredibly important brainwave for your health. In this state, you will be deeply asleep, but not actively dreaming. Your body needs this state to heal and regenerate. On a daily basis, you’ll need to achieve this state when you sleep at night to make sure your body can heal itself. When you’re feeling really sick or your body and mind are working hard, you’ll want to stay in this state a little longer.
A crossover RCT of a single session of theta stimulation in four healthy adults reported no significant improvement in verbal fluency or attention associated with the intervention and a reduction in immediate recall. Controlled comparisons reported significant benefit from the intervention in all three outcomes measured. Six pre/post studies reported significant benefit from the intervention for 19 of 28 cognitive outcomes.