“The great neuroscientist W. Gray Walter carried out a series of experiments in the late forties and fifties in which he used an electronic stroboscopic device in combination with EEG equipment to send rhythmic light flashes into the eyes of the subjects at frequencies ranging from ten to twenty five flashes per second. He was startled to find that the flickering seemed to alter the brain-wave activity of the whole cortex instead of just the areas associated with vision. Wrote Walter, “The rhythmic series of flashes appear to be breaking down some of the physiologic barriers between different regions of the brain. This means the stimulus of flicker received by the visual projection area of the cortex was breaking bounds— its ripples were overflowing into other areas.”
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.
In order to understand brainwave entrainment you first have to understand something about brain waves and electroencephalograms (EEG). Neurons are cells that communicate with each other through electrical conduction. When a neuron fires it creates a small electrical and magnetic field. These fields are far too small to measure by placing electrodes on the scalp, or even on the surface of the brain. The only reason we can detect the electrical fields of the brain is because many neurons are firing together – in synchrony. All brain waves that are measured by an EEG, therefore, represent a large group of neurons firing together.
If you’re operating in Alpha mode, you’ll feel very present and in the moment. You might be somewhat reactive to the world around you, but you’ll feel like you have time to process what’s going on rather than just react on instinct. This is a wonderful state to achieve when meditating or doing something that requires coordination, focus and learning.
Well, except for one reason: The power of suggestion. If I give you a music track and tell you that it will cure your headache, you're more likely to report that it cured your headache than you are to say "Well it didn't effect my headache, but it made my short-term memory better." An interesting experiment would be to buy a binaural track claimed to induce drunkenness, for example; play it for five friends without telling them the claim, and then ask how it made each of them feel. Give them multiple choices to select from. Chances are they're going to respond all over the map. If you have a friend who is a believer in binaural beats, I suggest going ahead and setting up this little test.
Move your focus to the sole of your right foot. Tune in to any sensations you feel in that part of your body and imagine each breath flowing from the sole of your foot. After one or two minutes, move your focus to your right ankle and repeat. Move to your calf, knee, thigh, hip, and then repeat the sequence for your left leg. From there, move up the torso, through the lower back and abdomen, the upper back and chest, and the shoulders. Pay close attention to any area of the body that causes you pain or discomfort.
...  While entrainment by binaural auditory beats in the alpha frequency has also been shown to enhance creativity, cognition, memory, and an improvement in intelligence tests and achievement tests in learning disabled boys.  The gamma-band activity has been shown to involve in a variety of functions such as attention, memory, and consciousness. Current literature suggests that entrainment by gamma beats promotes cognitive flexibility, modulates visual attention, and enhances creativity. ...
Theta: This brainwave pattern is associated with deep relaxation and with some stages of sleep, including the lighter stages of non-REM (NREM) sleep. REM sleep itself is mostly composed of beta wave and other activity that’s similar to an alert, waking brain. Deep meditation produces theta waves, which are slower and lower frequency (between 5-8 hertz) than Alpha waves. That murky barrier between sleep and wakefulness, when you’re drifting in and out of sleep, and your thoughts feel dreamlike and difficult to remember? That’s a theta-dominant state of consciousness.
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.