^ Bittman, B. B., Snyder, C., Bruhn, K. T., Liebfreid, F., Stevens, C. K., Westengard, J., and Umbach, P. O., Recreational music-making: An integrative group intervention for reducing burnout and improving mood states in first year associate degree nursing students: Insights and economic impact" International Journal of Nursing Education Scholarship, Vol. 1, Article 12, 2004.

Let’s say you’re listening to a sound in your left ear that’s at a frequency of 132 Hertz (Hz). And in your right ear, you’re listening to a sound that’s at a frequency of 121 Hz. Your brain, however, gradually falls into synchrony with the difference — or 11 Hz. Instead of hearing two different tones, you instead hear a tone at 11 Hz (in addition to the two tones given to each ear).
Further research in the mid-1990s examined claims that binaural beats can provide the listener with an experience akin to that of taking recreational drugs, stop them from smoking, help them lose weight, and other similar claims (often referred to under the umbrella term “brainwave entertainment”). Unfortunately, at this time, science has not been able to definitively prove that these claims are true, although there is, in some cases, powerful anecdotal evidence suggesting that for some individuals, these beneficial effects are very much a reality.
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. 

Many people experienced in using alpha brainwave entrainment report that the state of mind associated with alpha waves is a time when they feel most consciously connected to their subconscious mind. The intense experience of hypnagogic sleep, reported by some people as a feeling of being awake and asleep at the same time, is also associated with alpha brainwaves.
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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 quite different phenomenon results when stereophonic earphones are used and the signals are applied separately to each ear. Under the right circumstances beats can be perceived, but they are of an entirely different character. They are called binaural beats. . . . Binaural beats require the combined action of both ears. They exist as a consequence of the interaction of perceptions within the brain.”
You don't have to buy one, though. It's not too hard to make your own binaural beat, and free software is widely available to do just that. The one that I used to make that little sample is an open-source program called Gnaural, available on the Sourceforge website. It's pretty easy to use, though it takes some practice before you can generate some of the really cool, more professional sounding beats. A binaural beat consists of two simple tones, and most people add that background pink noise. Nothing special.