Binaural beats are the playing of two sine waves of close, but not the same, frequency into different earpieces of a set of headphones. The "beat" is heard as the brain tries to process them as a distinct sound, while taking into account the constructive/destructive interference. It is said to migrate brain waves to be closer to that frequency, like a sort of biological resonance, which is true. Of course the same can be said for listening to relaxing music help you relax, up tempo music to help you feel energetic, etc...
Basically, "two ears." One usage of the word is "binaural recording," which is a form of stereo recording meant to take advantage of the spatial perception of the human ear. Recordings are usually done using a pair of microphones mounted to a dummy head with roughly accurate models of the human outer ear, and the result when played back through headphones is extremely realistic and comparable to surround sound, though following an entirely different recording model. Binaural recordings aren't woo at all, and have nothing to do with binaural beats.
♥ I've beeen training in self-hypnosis for a while (under supervision and for a reason) and found that the 8-4 Hz beats put me very quickly in a deeply relaxed state. Definitely the thing! With the timer, I can shut them for the real self-hypnosis. I haven't tried the other beat generators yet, but this one works much better than I expected and clearly does the job. In a few words: I'm impressed!
In the average person, the activity of one brain hemisphere is dominant over the other, called brain lateralization. This hemispheric imbalance leads us to experience the world in a black and white way, perceiving separation over connectedness. When brainwave entrainment is used to synchronize brainwave activity in both hemispheres simultaneously, a person can more easily integrate information from all parts of the brain and solve problems with greater intelligence and sensitivity.
Beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the third harmonic (i.e. second overtone) of the bass note beats with the second harmonic (first overtone) of the other note. As well as with out-of tune notes, this can also happen with some correctly tuned equal temperament intervals, because of the differences between them and the corresponding just intonation intervals: see Harmonic series (music)#Harmonics and tuning.
If brainwave entrainment leaves you with unwanted side-effects (see below) or discomfort, you’re probably encouraging a range of brainwaves that are already excessive in some area of your brain. The way around this is to get a brain map to see what your brain’s strengths and weaknesses are, and see what (if any) brainwaves could use some encouragement.