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:
Although the binaural beats / music / downloads on this site contribute to wellness, they are not intended as a replacement for medical or psychological treatment. No medical claims are intended express or implied. Despite the fact that all statement made on this website are supported by research, no statements have been evaluated or approved by the U.S. Food and Drug Administration or any other international governance responsible for health care.
Transparent Corp's Research Area is arguably the most comprehensive resource for collated brainwave entrainment research.   Update: the main research area on Transparent Corp's website is currently being updated, so it is offline.  However, you can still access their peer-reviewed research paper as a PDF here: “A Comprehensive Review of the Psychological Effects of Brainwave Entrainment“.
A more extensive study of over 100 participants who were undergoing general anesthesia for a day procedure, reported a decrease in pre-operative anxiety. The participants in this study listened to 30 minutes of binaural beats before surgery, but the researchers noted that people experiencing high levels of pre-operative anxiety could listen to binaural beats for up to 1 hour before anesthesia to reduce levels of anxiety.
Hey, even before we spoke about creating Journey, I was thinking about how people across the world do their spiritual practices and the commonalities between them all. I was thinking, there is the path of stillness—which links right back to what we were talking about getting to a state of deep, profound relaxation and bringing clarity into stillness. Then there’s the path of rhythm, of rocking, of dancing. But there’s always a rhythm to it—even in the movements of Tai Chi, there’s a smoothness, a smooth rhythm. What it never is, is arrhythmic—those are the movements of a more anxious, frightened animal kind of thing. 
In addition, Western culture reinforces thought and communication styles associated with the left brain hemisphere, which controls logic, language, and linear thinking in a majority of people, as opposed to the right hemisphere which controls brain centers for emotional, intuitive, creative, and non-linear thought processes. Note that a significant minority of people has the opposite hemispheric dominance than the majority of people.
Theta brainwaves in the frequency range of 6 to 9 hertz are known as thalpha waves because of their proximity to alpha waves. They are seen during states of high suggestibility, during hypnosis, and during paranormal experience and are also connected to an increase in human growth hormone (HGH) levels and higher blood flow to the brain. Theta brainwaves sit between the realms of the subconscious and conscious mind, making them an especially useful brainwave state for developing creative thinking, working through emotional problems, and integrating subconscious and conscious experience. 
A therapy that slows brainwave activity, helping to produce low-frequency waves, is likely to aid relaxation and sleep. But it’s not only lowering brainwave frequency that binaural beats may offer to sleep and relaxation. A small study (19 people) has found that exposure to binaural beats is associated with changes to three hormones important to sleep and well being:
Despite the vast differences between each individual, our brain’s inner workings are remarkably similar. Brainwave Entrainment was built around these fundamental similarities and has equally powerful effects for almost everyone who uses it. While each situation may require a different frequency or audio track, Brainwave Love has one of the most complete, effective libraries to cover your every need. Take a look now:
Meanwhile, the therapeutic benefits of listening to sound and music is a well-established principle upon which the practice of receptive music therapy is founded. The term 'receptive music therapy' denotes a process by which patients or participants listen to music with specific intent to therapeutically benefit; and is a term used by therapists to distinguish it from 'active music therapy' by which patients or participants engage in producing vocal or instrumental music.[37] Receptive music therapy is an effective adjunctive intervention suitable for treating a range of physical and mental conditions.[38]
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