When a sound reaches your ears, your brain instantly works to determine where that sound came from from. If your hear a noise that originated slightly to your left, then the sound will not only be a little louder in your left ear, it also arrives at your left ear a few milliseconds sooner than it arrives at your right ear. You may not notice this effect on a conscious level, but your brain certainly does.
So your brain is very sensitive to small variations in the frequency of sounds, and to the way those sounds reach your ears.
When you listen to binaural beats, your brain is subjected to an effect that is perceives as a constant fluctuation in the directionality of the sound. This is really just an auditory illusion.
The rate of this fluctuation can be controlled by the use of specific sound frequencies. For example, by playing a tone of 200 Hz in the left ear, and 210 Hz in the right ear, a fluctuation of 10 Hz is detected by the brain.
The difference between the two frequencies could be called a "sub harmonic" – a sound that is below the threshold of human hearing. However, this sub-harmonic binaural frequency may still be detected as a slight pulsing sound. This pulsing, or beating, is why we call them binaural "beats".
Binaural beats cause the brain to adjust its dominant frequency to match the sub harmonic frequency of the beating sound. This is what is known as the "frequency following response".
We can take advantage of the frequency following response by creating binaural frequencies that help to induce specific brainwave frequencies. For example, we know that someone who is in a state of deep meditation may have a dominant brainwave frequency of say, 6 Hertz (6 cycles per second). When you listen to binaural tones that have been programmed to produce a 6 Hertz sub harmonic frequency, your own brainwaves will follow the frequency of the beat, and will naturally adjust in sympathy.
In other words, binaural frequencies can be used to adjust the dominant frequency of your own brainwaves, leading to altered states of consciousness, from light relaxation, to deep sleep. Most commonly they are used to accelerate and deepen meditation.
By themselves, binaural tones sound rather plain, and for that reason they are usually blended with soothing music or nature sounds.