Binaural beats change the frequency of your brainwaves, giving you control over which category you experience at any given moment. And because you’re in the driver’s seat — and producing specific frequencies to induce a specific state of mind — you can use binaural beats to boost performance, increase focus, get better sleep… the possibilities are endless. “There’s an infinite number of variations on how you could use this kind of technology,” says Bill Harris, Director of Centerpointe Research Institute and creator of auditory brainwave training program Holosync.
The effects are strongest while you are listening to the tones because your brainwaves are synchronized and tuned into the frequency range you desire at that time.  After you've stopped listening the effects can still linger for a while afterwards.  The timescale will vary from person to person and be affected by what you do after you've stopped listening.

Besides scientific literature, some authors have written of the promising research on meditation in books targeted for general audiences. One such book, Buddha’s Brain by Rick Hanson, PhD shares the current scientific research and investigations into meditation.[19] Hanson, a neuroscientist and researcher, explains to readers the scientific studies in plain language and discuss the impact of the results. Hanson’s main argument is that positive emotions, like love can be strengthened through meditation in a neuroplastic manner, citing dozens of scientific studies to support this claim.[19] Hanson’s viewpoint is representative of a larger popular movement to study and embrace Eastern phenomena including meditation in the Western world.
Over the long term, traditional eastern methods (such as meditation and yoga) train your brainwaves into balance. Of the newer methods, brainwave entrainment is an easy, low-cost method to temporarily alter your brainwave state. If you are trying to solve a particular difficulty or fine-tune your brainwave function, state-of-the-art brain training methods like neurofeedback and pEMF deliver targeted, quick, and lasting results.  
But what would be the point of generating a beat that was at the same rate as a certain brainwave frequency? First, consider that these frequency bands relate to different states of awareness. Delta is seen in deep sleep, theta in lighter stages of sleep, alpha when we are relaxed with eyes closed, and beta when we are awake and alert. Second, the main idea behind using binaural beats to help a person relax and sleep is that of entrainment. Entrainment means that a biological process is matched to some external stimulus. For example, our circadian clock is entrained to the day/night light cycle and helps the body organize physiological processes in an appropriate way over the course of the day. A repetitive sound at the frequency of a certain brainwave band could theoretically cause the brain waves to be entrained to that frequency and thus help induce the state associated with that brainwave band. This could have therapeutic utility.

Cortisol is an arousal hormone, stimulating alertness and attention. Cortisol levels rise and fall in connection to circadian rhythms—cortisol levels rise to their peak levels first thing in the morning, just in time for you to be active for the day. Too-high cortisol levels are associated with insomnia, as well as more time spent in light sleep, rather than deep sleep.
In 1973, biophysicist Dr. Gerald Oster published a famous article in Scientific American titled “Auditory Beats in the Brain”, which found that when two pure tones of varying frequencies were combined, a third rhythmic beat was created which he called binaural or monaural beats. According to Oster, monaural beats occur when two tones are combined and sent through a loudspeaker, while binaural beats occur when stereo headphones are used to deliver each tone separately to each ear. Oster concluded that monaural beats were a more effective form of brainwave entrainment.
Passively listening to binaural beats may not spontaneously propel you into an altered state of consciousness. One's subjective experience in response to binaural-beat stimulation may also be influenced by a number of mediating factors. For example, the willingness and ability of the listener to relax and focus attention may contribute to binaural-beat effectiveness in inducing state changes. "Ultradian rhythms in the nervous system are characterized by periodic changes in arousal and states of consciousness (Rossi, 1986).
Please note: When you take one earphone out, move it as far away from your ear as possible. With some headphones you may still be able to hear the pulsating sound if the removed headphone is still fairly close to your ear; this is because your brain can still detect the frequency vibration coming from the headphone. In addition, push the earphone that’s still on your ear tightly to your ear, while moving the other earphone as far away as possible.