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.
Meditations that cultivate mindfulness have long been used to reduce stress, anxiety, depression, and other negative emotions. Some of these practices bring you into the present by focusing your attention on a single repetitive action, such as your breathing or a few repeated words. Other forms of mindfulness meditation encourage you to follow and then release internal thoughts or sensations. Mindfulness can also be applied to activities such as walking, exercising, or eating.

For those who accept that we are spiritual beings currently experiencing a physical existence, with consistent practice of meditation and brainwave entrainment, you get all of the above, plus; a deeper feeling of connection and oneness with all things; a heightened sense of relationship with the Divine, whether you believe in an anthropomorphic God or just an All-Inclusive Presence; more peace and confidence in the Divine and less reliance on dogmatic policies and practices (this is not to say that dogma and ritual do not have their proper time and place!); more freedom from the fear of death; greater hope for that which comes after this life; a greater appreciation for and sense of relationship to others, even when others act in ways that are not in our personal best interests, and much, much more.
There is a lot to like about this technology as a potential treatment for sleep problems. It’s low impact and non-invasive, it doesn’t rely on chemical drugs, it’s inexpensive and for most people likely easy to adopt and maintain. In this way, it’s similar to the other behavioral therapies for sleep that I like so much, including meditation and relaxation techniques, and other mind-body therapies.
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.  
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.

Listening to brainwave entrainment music will provide you with the benefits of a formal meditation practice. It will improve your mental clarity, your creativity and your ability to learn and to concentrate. It will bring you peace of mind and emotional stability. It is also one of the most powerful natural ways to cure insomnia and can dramatically improve the quality of your sleep.
One can also learn to control and slow down their brain waves through various neurofeedback technologies such as electroencephalograph (EEG), galvanic skin response (GSR), and heart, pulse and breath rate monitors. These devices measure stress and relaxation parameters and then "play" back the signals to the user so they can use the signals as a beacon to guide and "steer" themselves into a relaxed state. This takes some time, work and discipline but is much quicker than learning meditation.
For those who accept that we are spiritual beings currently experiencing a physical existence, with consistent practice of meditation and brainwave entrainment, you get all of the above, plus; a deeper feeling of connection and oneness with all things; a heightened sense of relationship with the Divine, whether you believe in an anthropomorphic God or just an All-Inclusive Presence; more peace and confidence in the Divine and less reliance on dogmatic policies and practices (this is not to say that dogma and ritual do not have their proper time and place!); more freedom from the fear of death; greater hope for that which comes after this life; a greater appreciation for and sense of relationship to others, even when others act in ways that are not in our personal best interests, and much, much more.

Subsequently, the term 'entrainment' has been used to describe a shared tendency of many physical and biological systems to synchronize their periodicity and rhythm through interaction. This tendency has been identified as specifically pertinent to the study of sound and music generally, and acoustic rhythms specifically. The most ubiquitous and familiar examples of neuromotor entrainment to acoustic stimuli is observable in spontaneous foot or finger tapping to the rhythmic beat of a song.
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