Going deeper into a trance-like state of meditation, you enter the mysterious Theta state where brain activity slows almost to the point of sleep, but not quite. Theta is one of the more elusive and extraordinary realms you can explore. It is also known as the twilight state which you normally only experience fleetingly upon waking, or drifting off to sleep.
While originally brainwave entrainment was achieved by using pure tones of sound, it is now possible to take these tones and blend them with music, rhythms, and natural sounds, such as the sounds of flowing water, bird sounds, or waves lapping on a beach, creating extended tracts of varied and intriguing brainwave entrainment music for everyday use.

♥ Imagine a really bad ringing in your ear and the pain that it brought along or when your ear was throbbing with pain. Can you remember the sound coming from that ear? Probably not, since the pain was probably far more memorable. This sounds very similar to that, but it is not at all painful. Quite a unique experience, really. Try it out, but you need to be wearing earphones and have the volume up.
Studies have shown binaural beats may affect levels of dopamine, a hormone that plays a broad role in cognition and a particular role in creative thinking. This has scientists examining the possibility that binaural beats can be used to stimulate creativity. (If you’re looking to be more creative and innovative in your thinking, keep in mind that sleep itself is a powerful tool!)
There are differences between high (over 18 hertz), mid (15 to 18 hertz), and low range beta states (12 to 15 hertz). Low beta states are more relaxed while still being focused, making this a good range for many daily work related tasks like balancing a checkbook, making a shopping list, or driving to a new place. However, people with attention deficit disorder lack the mental focus for doing these types of activities, and studies have found people with ADD are often low in this range of beta brainwaves.
Entrainment is a term originally derived from complex systems theory, and denotes the way that two or more independent, autonomous oscillators with differing rhythms or frequencies, when situated in a context and at a proximity where they can interact for long enough, influence each other mutually, to a degree dependent on coupling force, such that they adjust until both oscillate with the same frequency. Examples include the mechanical entrainment or cyclic synchronization of two electric clothes dryers placed in close proximity, and the biological entrainment evident in the synchronized illumination of fireflies.[13]
Critics, like Owen Flanagan, PhD, believe that Hanson, and those like him, are overextending the results of current scientific studies.[citation needed] In his book Bodhisattva’s Brain: Buddhism Naturalized, Flanagan presents a more conservative viewpoint of current scientific research and cautions readers against the seemingly exciting results of recent studies.[20] Flanagan does not believe current science supports the idea that positive emotion can be strengthened in the same way that stroke victims can recover use of limbs with use.[20] Flanagan does acknowledge that meditation may be beneficial in some way, but the mechanism of how meditation affects the brain is still clouded.[20] Similarly, Awasthi argues that Meditation is non-specific to the research studies showing clinical efficacy in some cases, though mechanisms remain unclear.[21] Flanagan and Hanson use many of the same scientific studies to attempt to support their differing viewpoint, but both authors identify the need and importance of future studies investigating meditation.

The most common way to use a brainwave entrainment is for a short-term benefit, to help guide your brain into a particular mental state at the time you need it.  In a similar way to how you might take a sleeping pill before bed to help you get to sleep, or maybe drink some coffee or an energy drink to help wake you up and give you a boost of energy.
A binaureal beat is created by playing a different tone in each ear, and the interference pattern between the slightly differing frequencies creates the illusion of a beat. It's intended to be heard through headphones, so there's no cross-channel bleed across both ears. Listen to this, I'll play a simple binaural beat, and I'll slide the pan control back and forth from one ear to the other. You can see that there isn't actually any beat, it's just an acoustic illusion: