While a practical understanding of brainwaves has been around for as long as people have been singing, chanting, and drumming, a scientific view of the electrical activity inside the human brain was not published until 1924 when German psychiatrist Hans Berger developed a machine for sensing and recording activity in the brain by attaching small electrical sensors to the scalp of his patients and recording the resulting electrical activity. Berger’s inventions and discoveries were built upon the earlier work of Richard Caton who published animal studies on brainwave oscillations in 1875.
Brain wave entrainment is a real phenomenon and is useful as one method of investigating how the brain works. But there is no evidence, nor any theoretical basis, for any long lasting effect on brain function or that there is any benefit of any kind. Despite this, there is a huge industry of devices that claim to train your brain waves and have a beneficial effect. I wouldn’t waste a dime on any such device.
However, yoga and meditation take time to learn and master, and until the student becomes proficient, progress can be slow and frustrating, leading many people to abandon the effort before they see the benefits. Brainwave entrainment has the potential for helping a person enter the relaxing and rejuvenating mind-states brought about by yoga and meditation without the learning curve and time needed for mastering these other techniques. Brainwave entrainment may even facilitate learning other mindfulness methods by helping a person achieve success faster and more reliably. 
Entrainment is like priming the pump of meditation. It doesn’t “cause” meditation any more than pouring that little bit of water into the pump initially “causes” water to appear in the well. The water was already there. The conditions for the pump to do its job just needed to be set up. What entrainment does is to create the conditions and the internal environment typically associated with meditation. You could get to that point without entrainment, certainly, but the entrainment allows you to get there quicker, more consistently, and to remain there for longer periods of time than you would ordinarily be capable of doing on your own.
The functional role of neural oscillations is still not fully understood;[6] however they have been shown to correlate with emotional responses, motor control, and a number of cognitive functions including information transfer, perception, and memory.[7][8][9] Specifically, neural oscillations, in particular theta activity, are extensively linked to memory function, and coupling between theta and gamma activity is considered to be vital for memory functions, including episodic memory.[10][11][12]
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