There are five main categories of brainwave frequencies: Gamma (40Hz+), Beta (13 – 40Hz), Alpha (7 – 13Hz), Theta (4 – 7Hz), and Delta (<4Hz). Each category is associated with a different state of mind; so, for example, when you’re in a peak state of performance, your brain produces Alpha Waves, and when you’re in a deep sleep, your brain produces Delta Waves.
All of this is entirely understandable, even somewhat predictable. Unfortunately, it quickly becomes counter-productive. Such experiences, while having a certain feeling of solidity to them, are largely the product of our desires and expectations. Did your face get flushed? One look in the mirror confirms it did. Was this caused by the entrainment? No, it was not. It was the result of what was sought after and what was expected or even hoped for.
People who meditate regularly enjoy many benefits such as increased sense of well being, happiness, contentment, and far less anxiety that many other people. Some believe that this is due to both hemispheres of the brain being in sync with each other, which meditative practice can provide. Therefore, a goal of using technology to entrain the brain and align the frequencies of the brain hemispheres has become a very interesting avenue of science and experimentation.

Our everyday, waking brain used for active intelligence operates at approximately 13 hertz, which is in the range of high alpha or low beta frequencies. People who have certain learning disabilities and problems with attention often have low levels of 13 hertz frequency brainwaves in crucial areas of the brain used for sequencing tasks and doing simple math calculations. This is one concrete example of how brainwaves are associated with thinking and behavior. Each identified brainwave frequency has a different effect on a person’s ability to think, act, and feel.
So, in summary, binaural beats certainly do not work the way the sellers claim, but there's no reason to think they're any less effective than any other music track you might listen to that effects you in a way you like. If they make you sleepy (like they all do for me), use them to go to sleep. If they relax you or get you amped, use them for that. But don't expect them to be any more effective than regular music. If someone you know claims that they are, put them to the test, and bust the myth.

Some people believe that using this stuff can be a replacement for meditation. While sitting passively and listening to something that can give you the same effect frequency-wise as meditation, there is still far more benefit to meditating than just entrainment. Meditation and mindfulness allow you to really understand yourself on a level far deeper than technology will bring you.
Resonant entrainment of oscillating systems is a well-understood principle within the physical sciences. If a tuning fork designed to produce a frequency of 440 Hz is struck (causing it to oscillate) and then brought into the vicinity of another 440 Hz tuning fork, the second tuning fork will begin to oscillate. The first tuning fork is said to have entrained the second or caused it to resonate. The physics of entrainment apply to bio-systems as well. Of interest here are the electromagnetic brain waves. The electrochemical activity of the brain results in the production of electromagnetic wave forms which can be objectively measured with sensitive equipment. Brain waves change frequencies based on neural activity within the brain. Because neural activity is electrochemical, brain function can be modified through the introduction of specific chemicals (drugs), by altering the brain's electromagnetic environment through induction, or through resonant entrainment techniques.
Science shows that massages reduce stress, but you don’t have to go to the spa—you can give yourself one right now. “Learning how to self-massage your foot, head, neck, or shoulders reduces the stress hormone cortisol, boosts your immune system, and increases the feel-good hormones oxytocin, dopamine, and serotonin,” Dr. Serani says. You can even use a tennis ball or cold water bottle on your feet or neck. In addition, try rubbing pressure points like the webbing between your thumb and index finger, or your inner wrist. Another technique is the EFT tapping technique, literally tapping certain points on your body such as in between your eyes, your temples, and the center of your collarbone. “Tapping brings cleansing energy to the meridian points, as your mind directs the energy to what’s unbalanced in the body,” Whitaker says. “This restores your mind and body’s natural balance, which aids in releasing stress, worry, fears, and disharmony.”
All techniques, whether mantra, focus on the breath, contemplation of a koan, or any other, are simply the vehicles we use to take us into (hopefully) a meditative state. Put another way, the purpose of repeating a mantra is not to get proficient at repeating a mantra. The purpose is to take us to a meditative state where the mantra slips away and is no longer necessary.
This is probably the most popular choice of frequency. The theta state is a state of tremendous stress relief. The benefits associated with theta level relaxation include improved concentration, reduced hyperactivity and improved memory. While in a state of theta relaxation, one’s blood pressure, breathing and heart rate all slow to a much more restful and healthy level that promotes natural healing. During theta relaxation one may also experience vivid flashes of mental imagery as the mind opens to memories or subconscious information that is not available to the conscious mind during the normal waking state. The theta state is a very deep state of relaxation that is excellent for deep hypnosis and mental programming.

In addition to its calming physical effects, the relaxation response also increases energy and focus, combats illness, relieves aches and pains, heightens problem-solving abilities, and boosts motivation and productivity. Best of all, anyone can reap these benefits with regular practice. And while you may choose to pay for a professional massage or acupuncture session, for example, most relaxation techniques can be done on your own or with the aid of free audio downloads or inexpensive smartphone apps.
This music encourages a state of delta relaxation. Delta brainwaves are most prevalent during deep, dreamless sleep. The delta state is a mostly unconscious state that is essential to one’s physical, emotional, psychological and spiritual wellbeing. People who are able to achieve a state of delta relaxation through meditation will sometimes describe spiritual encounters and out of body experiences. The delta state is perfect for inducing profound spiritual experiences, healing and deep subconscious repatterning. Delta frequency brainwave entrainment music is also a fantastic cure for insomnia.
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.