Brainwaves are the collective electrical signal of millions of neurons working together in a living brain, producing our sense of alertness – or lack thereof - and producing our experience of reality. As brainwaves change, so does our perception of the world and our inner perception of ourselves. By learning to control our brainwaves, we can achieve specific, desirable mental states, such as feeling more relaxed, less anxious, more creative, more focused, or sleepier.
Binaural beats is a method where two sound waves of different frequencies are introduced into each ear. These frequencies when processed by the brain cancel each other out, creating a whole new frequency. So if we had a tone of 500 Hz in one ear and a 510 Hz tone in the other, the result would be a 10 Hz tone. So while a 10 Hz tone couldn’t be directly heard, using binaural beats we can create that tone inside our brain.
Despite the lack of solid evidence of the effectiveness of binaural beats in producing brainwave changes, and that those changes can be effective in altering our conscious states, there do exist hours of recorded binaural beat videos available on YouTube. Some of these are just straight beats designed to ease the listener into various states by gradually varying the frequencies of the beats. A nice example of this can be found in a 90-minute video by Jody Hatton. Others embed the beats into a musical score, which some people find easier to listen to. Spotify has a whole playlist devoted to binaural beats. You can try these and many others to see if this is something that may be helpful to you. The soothing nature of the sounds may be what really helps, but that’s fine if you just want to relax and drift off to sleep. You can also find quite a few apps that generate binaural beats at your phone’s app store. If you want to relax and sleep just be sure to set the frequency in the theta range (4 – 7 Hz). Patients have reported to me that they felt energized or even anxious after listening to a few minutes of the beats, but this was usually because they were set to a high frequency like beta (13 – 16 Hz). Be sure to try listening to the beats for a short time and if they have a negative effect, just stop listening. If you find them helpful, that’s great, and you have a new technique that can be used to promote relaxation, something most of us can use. 
Binaural beats are auditory brainstem responses which originate in the superior olivary nucleus of each hemisphere. They result from the interaction of two different auditory impulses, originating in opposite ears, below 1000 Hz and which differ in frequency between one and 30 Hz (Oster, 1973).For example, if a pure tone of 400 Hz is presented to the right ear and a pure tone of 410 Hz is presented simultaneously to the left ear, an amplitude modulated standing wave of 10 Hz, the difference between the two tones, is experienced as the two wave forms mesh in and out of phase within the superior olivary nuclei. This binaural beat is not heard in the ordinary sense of the word (the human range of hearing is from 20-20,000 Hz). It is perceived as an auditory beat and theoretically can be used to entrain specific neural rhythms through the frequency-following response (FFR)--the tendency for cortical potentials to entrain to or resonate at the frequency of an external stimulus. Thus, it is theoretically possible to utilize a specific binaural-beat frequency as a consciousness management technique to entrain a specific cortical rhythm.  
Theta waves have another interesting characteristic. The Earth has a measurable resonance of 7.83 hertz known as the Schumann resonance. Because the Schumann resonance is a constant background frequency surrounding all life, it may play a special role in biological activity. The Schumann resonance frequency falls within the range of theta brainwaves and may have something to do with why these brainwave frequencies are so powerful. 

"These methods are often described as nondirective, because practitioners do not actively pursue a particular experience or state of mind. They cultivate the ability to tolerate the spontaneous wandering of the mind without getting too much involved. Instead of concentrating on getting away from stressful thought and emotions, you simple let them pass in an effortless way."
There is a lot to like about this technology as a potential treatment for sleep problems. It’s low impact and non-invasive, it doesn’t rely on chemical drugs, it’s inexpensive and for most people likely easy to adopt and maintain. In this way, it’s similar to the other behavioral therapies for sleep that I like so much, including meditation and relaxation techniques, and other mind-body therapies.

These sounds in these musical tracks are presented through monaural beats, binaural beats, isochronic tones, or a mixture involving combinations of all three of these modalities, described in detail below. Choose alpha brainwave tracks for calming anxiety and relaxing body and mind, and choose theta tracks for help in getting to sleep and for bringing hidden feelings to the surface. Some people also report out-of-body type experiences when in theta brainwave states.

I have also noticed that during my morning meditation session (I use the product twice daily – once in the morning and again at night), I’m able to almost instantly reach extremely deep levels of relaxation. In fact, within minutes I lose all sensation in my extremities. This is exactly like yogic meditation’s pratyahara, or sense withdrawal, state. It’s really quite remarkable that I could get that relaxed that quickly. This process usually takes me anywhere between a half an hour and an hour and a half. With EquiSync, I reach the same state in literally 2 to 5 minutes!

(Shannahoff-Khalsa, 1991; Webb & Dube, 1981). These naturally occurring shifts may underlie the anecdotal reports of fluctuations in the effectiveness of binaural beats. External factors are also thought to play roles in mediating the effects of binaural beats (Owens & Atwater, 1995). The perception of a binaural beat is, for example, said to be heightened by the addition of white noise to the carrier signal (Oster, 1973), so white noise is often used as background. "Music, relaxation exercises, guided imagery, and verbal suggestion have all been used to enhance the state-changing effects of the binaural beat" (Owens & Atwater, 1995). Other practices such as humming, toning, breathing exercises, autogenic training, and/or biofeedback can also be used to interrupt the homeostasis of resistant subjects (Tart, 1975).

Once you have a good recording, start listening to your binaural beats while in bed, and try to be sure you’re undisturbed so your brain can sync up. If you have chronic insomnia, be sure to listen on a regular basis so you train yourself to fall asleep at the same time every night. If you like, you can even invest in a pair of comfortable sleep headphones.
I tried other companies the last few years or so….among the likes that mainly used binaural audio and the deepest I was really ever to achieve was alpha state….maybe theta once or twice over the last few years. It takes incredible dedication and practice to achieve the deep, renewing states of meditation that are most sought after…..I listened to the theta meditation mp3 last night and within what seemed like a few minutes my mind was flooded with imagery…memories long gone…my body was sleeping, heavy as lead, but my mind was crystal clear, aware of my surroundings. I could barely even open my eyes!
There is a solution, which, although you may not have heard about it, has been around (and scientifically tested!) for decades now. By using binaural beats, you can ease your brain from its active state into a more restful state simply by listening to a different frequency wavelengths of sound in each ear. Because two different wavelengths are entering through two different entrances (your ears), that difference is perceived as a “beat” (though it may sound like a warble to some) that resonates at the frequency equal to the difference. The brain will entrain (match) itself to the beat produced by the difference in wavelengths. If the difference between the two wavelengths is less than seven hertz, your brain will fall into a state of deep relaxation, also known at the theta range.
If you are reading this, it is likely that your Beta brainwaves are dominating your mind. Beta brainwaves are present when your attention is focused on a problem, whether that is working something complex out in your head, Focusing on a video game or having a conversation with another person. Beta waves are also experienced during anxiety, stress and excitement.2
A good recording will also not immediately start with tones that produce the theta range, but will begin higher up, in the beta range (which is associated with anxiety, but also active concentration and other waking states of being), and gradually move down, through the alpha range (which is the ideal meditative wavelength, but is also associated with falling asleep) before moving into the final, theta, range. If you get a binaural beat that goes directly into the theta range, you might find yourself distracted or unable to sync up as easily.
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.
"Wow! I have been doing this Awakening Kundalini guided meditation every morning for about two weeks now. I am a yoga teacher and I have never experienced energy like this before! Every morning, I feel a surge and abundance of endless vital energy nourish my mind, body, and soul. The sounds, theta waves and guidance are perfectly combined to gently awaken the sleeping serpent confirmed by the exquisite sensations experienced. "  --Katarine
As to the second question raised in the above paragraph, audio with embedded binaural beats alters the electrochemical environment of the brain. This allows mind-consciousness to have different experiences. When the brain is entrained to lower frequencies and awareness is maintained, a unique state of consciousness emerges. This state is often referred to as hypnogogia "mind awake/body asleep."  
But we don't need any studies to tell us that different people can listen to different kinds of music and be affected. A lot of people who work out have a workout playlist on their iPod that keeps them energized. Some people listen to certain music to help them fall asleep. The Muzak company has built an industry on relaxing music that will keep people in the mood to shop. Music does affect our mood, and so we already have every reason to expect binaural beat recordings to produce the same effect. Different people may find certain binaural beats to be relaxing or energizing. But, we've never found any reliable indication that a binaural beat's connection to our brain is any deeper or more meaningful than any other music track. We do know for a reasonable certainty that specific claims made by most sellers of binaural beats are not credible, and that there is no reason to think that the effect they're claimed to produce will work for you.