Gamma brainwaves occur during creative thinking and processing of memory and language and in many learning activities. These brainwaves are not present at all when a person is under anesthesia, but return as soon as the person becomes conscious again. Multiple scientific studies have shown gamma brainwave entrainment to be helpful for reducing distractibility, improving short-term memory, improving motor coordination, and relieving migraine headaches.
According to the Wikipedia entry “(i)n acoustics a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies.” Further, a binaural beat is “… an auditory illusion perceived when two different pure-tone sine waves, both with frequencies lower than 1500 Hz, with less than a 40 Hz difference between them, are presented to a listener dichotically (one through each ear)”. If the two frequencies are, say, 5 Hz apart as in 500 and 505 Hz, then a third tone at 5 Hz will be heard in addition to the two pure tones. What this technique allows for is the creation of an apparent auditory signal that can be perceived and that is at a predictable frequency. In this way, relatively low frequencies can be generated that can be easily perceived and that can correspond to the common brainwave frequency bands. These are often categorized as delta (0.5 – 4 Hz), theta (4 – 7 Hz), alpha (8 – 12 Hz), and beta (13 – 16 Hz). You may find somewhat different ranges and bands other than these listed depending on the source you consult. It is also possible to produce flashes of light that can be administered within these frequency bands but there is some risk of inducing seizures in susceptible individuals. While the most common frequency range for inducing seizures is 15 – 25 Hz, unfortunately, the possible range is 1 – 65 Hz, which covers essentially the whole range of standard EEG frequency bands. This makes use of sound stimulation safer than visual or combined audio/visual stimulation. 
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.
How does brainwave entrainment work? Consistent, precisely engineered audio frequencies in the form of binaural beats cause the brain’s frequencies to match the stimulus. Your brain perceives two beats with slightly different frequencies (which are inaudible to the ear) through your headphones. It takes the difference between the two, and matches its own frequency to it. This is called the “frequency following” response.
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You can experiment with the length of time you listen to the binaural beats to find out what works for you. For example, if you’re experiencing high levels of anxiety or stress, you may want to listen to the audio for a full hour or longer. Remember, you must use headphones for binaural beats to work. You may also want to listen with your eyes closed.
One problem with researching binaural beats is that listening to them does not guarantee brain entrainment. Although a determined listener should be able to focus on the beats enough to relax and let his or her brain match the binaural beat wavelength, sometimes, and for some people, it just won’t happen.  Also, some claims, such as astral travel, are not scientifically measurable at this time, and so are unverifiable in scientific studies. However, there are several studies that suggest that a meditative state is more easily attained when listening to binaural beats, suggesting that other such states may well be acheiveable too.
Do note the pre-sets slightly below to the right. Remember: Delta is for deep sleep. Theta is associated with dreaminess. Alpha is a blank or relaxed state of mind and Beta is when you’re active. Try to clear your mind of any thoughts and expectations, and set the volume to an acceptable level. You can play around, but try to give a minute or two for your state of choice. At first glance, you’d think this sounds like an alien spaceship, if not a microwave or a washing machine. Whatever it sounds like to you, if you give it an open mind you will notice there is something weird about this after all. Hopefully, your chosen frequency will have guided you towards the intended effect!

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Synchronized brain waves have long been associated with meditative and hypnogogic states, and audio with embedded binaural beats has the ability to induce and improve such states of consciousness. The reason for this is physiological. Each ear is "hardwired" (so to speak) to both hemispheres of the brain (Rosenzweig, 1961). Each hemisphere has its own olivary nucleus (sound-processing center) which receives signals from each ear. In keeping with this physiological structure, when a binaural beat is perceived there are actually two standing waves of equal amplitude and frequency present, one in each hemisphere. So, there are two separate standing waves entraining portions of each hemisphere to the same frequency. The binaural beats appear to contribute to the hemispheric synchronization evidenced in meditative and hypnogogic states of consciousness. Brain function is also enhanced through the increase of cross-collosal communication between the left and right hemispheres of the brain.

Most of these websites give some brief explanation of entrainment. The example you hear most often is that of Dutch polymath Christiaan Huygens, who in 1665, hung two pendulum clocks next to each other on a wall. He noticed that the pendulums eventually matched each others' frequency, but always in antiphase, opposite to each other, as if canceling each other out. He'd try disturbing one or setting them in sync, but they'd always return to the same antiphase synchronization. Huygen's experience is widely touted on binaural beat websites as a demonstration of how systems can become spiritually connected through some energy field. However, they misunderstand what happened, and have not read the full story. Huygens also tried taking one clock off the wall, and as soon as they were no longer physically connected to one another via the actual wall, the effect disappeared. It was not the proximity of the clocks to one another that created the entrainment; it was their physical, mechanical connection to one another. As each pendulum swung it imparted an infinitesimal equal and opposite reaction to the wall itself. With two clocks on the wall, the system naturally sought the lowest energy level, according to the laws of thermodynamics; and both pendulums would thus swing exactly counter to each other, minimizing the system's total energy.