The training process allows you to consciously access deeper levels of your brain and consciousness. Your whole brain power and function expands. You become intuitive, relaxed yet focused, creative, your thoughts become clearer and information processing improves more and more. The left and right brain hemisphere synchronizes and you'll start using the full power of your left (analitycal - logical - Intelligence) and right (creativity - imagination - visualisation) hemispheres together. To say that this helps in all imaginable areas of your life is an understatement. You'll also begin to discover deeper realities beyond the physical. You become happier, more relaxed and balanced.
Applying brainwave entrainment in the alpha range may result in benefits similarly found with Zen or Transcendental Meditation. These benefits extend throughout the body and include improved breathing patterns, higher physical energy levels, an improved outlook, increased sports performance, improved relationships, and increased workplace satisfaction and performance … just to name a few.

Other entrainment methods sometimes used include autopan modulation that moves sound in an 180º arc to create a desired tone. Harmonic box entrainment, invented by James Mann, uses a layering of binaural and monaural tones that alternate between ears, requiring headphones. Sound modulation and filtering, amplitude modulation, and pitch panning use diverse sounds to create rhythmic pulses matched to the desired brainwave frequency. 
The various mental states of the individual are thought to take place across a varied range of frequencies, or brainwaves. By encouraging the frequency following process, entrainment is able to create positive change in the brain, through matching carefully-selected frequencies of light and/or sound. The stimulus enables the individual to access a different state of consciousness, which can be useful for a number of benefits including relaxation, anxiety management, stress reduction and more.
A study published in Electroencephalography and Clinical Neurophysiology by Paul Williams and Michael West in 1975 examined the brainwave states of people experienced in meditation while using photic stimulation, and another study by Leonard, Telch, and Harrington in 1999 examined the successful use of brainwave entrainment techniques for attaining meditative states in subjects.
Have you ever found yourself in a tough situation where you couldn’t think of a way out? If you have, it might be due to a lack of Alpha brainwave activity. It’s been proven that increased production of these brainwaves allows people to deal with and solve problems at a faster rate and with far fewer difficulties. This is made possible thanks to the brainwave’s ability to get rid of “mental blocks” that prevent solving the problem at hand.
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“.
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.