When we are mentally active various groups of neurons will be firing and the EEG will look like a jumble of different waves at different frequencies. When we are in a relaxed state, however, our brains settle into a steady rhythm – when fully awake this is the alpha rhythm, which as a frequency of 8-12 hz and other recognizable features. When drowsy our brainwaves slow to the theta range, 6-7hz, and when in deep sleep into the delta range, 4-5hz.
Brainwave entrainment is a method which utilizes frequencies of the brain in order to bring about specific desired thoughts and behavior. In other words, brainwave entrainment is used to induce different brainwave states related to: enhanced focus, relaxation, sleep induction, meditation, etc. With the help of a specific stimulus, aural (audio), photic (visual) or the combination of the two, we naturally induce the brain to respond by synchronizing with the stimulus frequency; this is called the “frequency following response”. The assumption is that the human brain has a tendency to change its dominant Electroencephalography frequency (recording of electrical activity along the scalp) towards the frequency of a dominant external stimulus. This is why we also talk about “brainwave synchronization”.
When tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception[1], the beating starts to sound like a note, and a combination tone is produced. This combination tone can also be referred to as a missing fundamental, as the beat frequency of any two tones is equivalent to the frequency of their implied fundamental frequency.

When you play two separate frequencies in each ear, say 140 Hz and 149 Hz, the difference in frequency is 9 Hz. Your brain compensates for this difference and a third tone of 9 Hz is experienced. This will result in your brain being lowered or raised and tuned into the desired frequency. This is how binaural beats are produced. Headphones are essential for this to work.  

Over the long term, traditional eastern methods (such as meditation and yoga) train your brainwaves into balance. Of the newer methods, brainwave entrainment is an easy, low-cost method to temporarily alter your brainwave state. If you are trying to solve a particular difficulty or fine-tune your brainwave function, state-of-the-art brain training methods like neurofeedback and pEMF deliver targeted, quick, and lasting results.  
If brainwave entrainment leaves you with unwanted side-effects (see below) or discomfort, you’re probably encouraging a range of brainwaves that are already excessive in some area of your brain. The way around this is to get a brain map to see what your brain’s strengths and weaknesses are, and see what (if any) brainwaves could use some encouragement.