“Like the pulses of vibration that produce sound on a guitar string, your brain also creates pulses of vibrations. These vibrations are electrical impulses,” continues Naik. “Their activity can be measured by using an EEG (electroencephalogram), which measures the frequency of these pulses [which is measured in Hertz]. Your brain actually has a predominant frequency at which it operates in any given moment; this can be associated with your state of mind.”

For those who accept that we are spiritual beings currently experiencing a physical existence, with consistent practice of meditation and brainwave entrainment, you get all of the above, plus; a deeper feeling of connection and oneness with all things; a heightened sense of relationship with the Divine, whether you believe in an anthropomorphic God or just an All-Inclusive Presence; more peace and confidence in the Divine and less reliance on dogmatic policies and practices (this is not to say that dogma and ritual do not have their proper time and place!); more freedom from the fear of death; greater hope for that which comes after this life; a greater appreciation for and sense of relationship to others, even when others act in ways that are not in our personal best interests, and much, much more.

Some research suggests that the benefits from brainwave entrainment can last a lot longer, and still be seen for some time after you've stopped using it.  Study participants have still maintained improved test scores a few weeks after the stimulation had ceased.  Research on the long-term benefits has so far been minimal though, so how long the effects last is still up for debate.
To get a full answer you should really get in touch with the owner of the app, because it does really depend on how their track is constructed and how they intend it to work. I have one 50-minute sleep track which takes you down into delta (http://www.mindamend.com/shop/sleeping-and-dreaming/sleep-induction-isochronic-tones/) and that is designed to just get you to sleep, so you just let play until the end. If you played that track on repeat it might make you jump and wake you up, as the track begins at a higher frequency. I have another 8-hour sleep track which is meant to be played all throughout the night (http://www.mindamend.com/shop/sleeping-and-dreaming/deep-sleep-8-hour-sleep-cycle/). So it does depend on the individual track you are using.

Most of all, don't feel bad if you fall asleep. Your brain is still receiving many of the benefits of entrainment while you sleep through the audio tracks. In fact, many people report better, more restful sleep when they use brainwave entrainment to help them fall asleep. However, I recommend that you do not go to sleep with your brainwave track set to repeat, as that can be too much stimulation for the brain.
When your mind is all over the place, organizing your thoughts into a quick to-do list can help transfer the burden from your brain to paper. But for some people, seeing a long list of tasks can increase stress. Miller has another idea: a “stressor and action” sheet. “Fold a piece of paper in half length wise, and on the left column write ‘stressor’ and on the right hand column write ‘action,’” she says. “You will find as you write down thoughtful action steps to the things that are stressing you out, you regain authority over circumstance.” These are the signs you’re more stressed than you realize.

Brainwave entrainment music can be used almost anywhere and anytime, making this mood and self-improvement method versatile and flexible enough to do at work, while traveling, or at other times during the day. When used in the workplace during short rest periods, brainwave entrainment techniques can enhance concentration, communication, and work productivity.

“Binaural beats are not very noticeable because the modulation depth (the difference between loud and quiet) is 3 db, a two-to-one ratio. (Isochronic tones and mono beats easily have 50 db difference between loud and quiet, which is a 100,00-to-1 ratio). This means that binaural beats are unlikely to produce an significant entrainment because they don’t activate the thalamus.”
Gamma was dismissed as 'spare brain noise' until researchers discovered it was highly active when in states of universal love, altruism, and the ‘higher virtues’. Gamma is also above the frequency of neuronal firing, so how it is generated remains a mystery. It is speculated that gamma rhythms modulate perception and consciousness, and that a greater presence of gamma relates to expanded consciousness and spiritual emergence.
Researchers advise that people who suffer from epilepsy or seizures should ask for professional insight first before using binaural beats. Pregnant women are also advised to seek the advice of their physicians. However, I haven’t heard anything about binaural beats impacting those who have had heart attacks negatively. That being said, I encourage you to do extra research.
Brain waves are electrical activity patterns caused by the neurons of the brain communicating with each other. Brain waves can be detected using sensitive medical equipment such as an electroencephalogram (EEG) monitor. Brain waves provide an indication of the mental state of an individual. In other words, the appearance of brain waves is directly connected to what a person is doing, thinking or feeling. The different Brain states are: Gamma, Beta, Alpha, Theta, Delta. You have your own unique brain wave patterns that function habitually. Some of these brain wave habits are useful, and others need some fine-tuning. When your brain is functioning efficiently, your brain waves are “in sync” with your activity, but stress or lack of sleep can interfere with this natural harmonious relationship. To restore this harmony, at Gaia Meditation, we have developed a wide range of free audio programs, including meditation music, relaxation music, sleep music and plenty other Sound Healing programs.
I enjoy this one called: Cognition Enhancer For Clearer and Faster Thinking – Isochronic Tones (Electronic) … I seem to enjoy it. Any harm in just listening to this one every day for 30 minutes as a routine daily thing, just like brushing your teeth and making your bed. I would just use it at times when I’m working at my desk, maybe even reading the online news etc…Thoughts?
Sleep and stress tend to cause a vicious cycle – if you’re stressed, then you can’t sleep, which makes you ill-prepared to handle the stressors of the next day, leading to more stress. To relieve stress before bed, try some relaxation techniques (see below) and disconnect from technology as much as possible an hour before bedtime. To ensure the proper amount of rest (7-8 hours is recommended), set an alarm reminding you to go to bed.

There are general recommendations for stress management that can be applied in most situations. However, keep in mind that there are individual differences and preferences, so a “cookie cutter” approach should be avoided when making recommendations. A comprehensive stress management program will include specific techniques prescribed on an individual basis, but general stress management recommendations are presented in Table 2.
Although getting organized and staying organized is not often thought of as a stress management technique per se, this is an activity that can reduce the stress you face in your life, and can even be calming as you are engaged in the act. (See how cleaning can be a stress reliever in itself.) By working through the clutter of your life, you can eliminate those energy drains that can make you feel like you're 'being pecked to death by ducks' and reserve that energy for dealing with life's more important challenges. Read more on being organized and eliminating extra stress from your life. 
“In order to get into a flow state, you have to calm a part of the brain, the posterior cingulate cortex, which is the source of what brain scientists call the default state, which is the non-focused state,” says Harris. “At any rate, it turns out that Holosync [binaural beats], when you listen to it, [calms that part of the brain] and so does traditional meditation. It’s just Holosync does it faster and more easily and more effortlessly. It turns down the posterior cingulate cortex and it enhances the other part of the brain that, when it’s enhanced, you can easily go into a flow state.”
If you search the Internet for "binaural beats" you'll quickly find there's a whole industry built on the idea that listening to binaural beats can produce all kinds of desired effects in your brain. It can alter your mood, help you follow a diet or stop smoking, get you pumped up for a competition, calm you down, put you to sleep, enhance your memory, act as an aphrodisiac, cure headaches, and even balance your chakra. Binaural-Beats.com offers a $30 CD that they call the world's first "digital drug". They claim it can get you drunk without the side effects. I-Doser.com offers a range of music tracks that they say simulates a variety of actual pharmaceuticals, such as Demerol, Oxycontin, and Vicodin. Suffice it to say that no matter what superpower you're looking for, someone on the Internet sells a binaural beat audio file claimed to provide it.
When signals of two different frequencies are presented, one to each ear, the brain detects phase differences between these signals. "Under natural circumstances a detected phase difference would provide directional information. The brain processes this anomalous information differently when these phase differences are heard with stereo headphones or speakers. A perceptual integration of the two signals takes place, producing the sensation of a third "beat" frequency. The difference between the signals waxes and wanes as the two different input frequencies mesh in and out of phase. As a result of these constantly increasing and decreasing differences, an amplitude-modulated standing wave -the binaural beat- is heard. The binaural beat is perceived as a fluctuating rhythm at the frequency of the difference between the two auditory inputs. Evidence suggests that the binaural beats are generated in the brainstem's superior olivary nucleus, the first site of contra-lateral integration in the auditory system (Oster, 1973). Studies also suggest that the frequency-following response originates from the inferior colliculus (Smith, Marsh, & Brown, 1975)" (Owens & Atwater, 1995). This activity is conducted to the cortex where it can be recorded by scalp electrodes.  
Entrainment is a physics principle in which one rhythmic system falls in synchrony with another rhythmic system. If you’ve ever found yourself moving your body to the beat of your favorite song, then you’ve experienced entrainment in its most basic form. Besides music, this principle can be found all around you, probably more than you realize. Here are a few examples:
Because of the way they are created, there may be a positive benefit from listening to binaural beats without considering the brainwave entrainment aspect, but I haven’t seen any research on that. I first discovered brainwave entrainment through binaural beats about 10 years ago now, but they didn’t do anything for me. So I’ve never been a regular user of them. I believe isochronic tones are a more effective way to produce hemispheric synchronisation because they produce a much stronger response in the brain
It is important to note that not all stress is bad. Everyone experiences a certain amount of stress on an almost daily basis, and it cannot be completely eliminated. Stress becomes a problem when too much is experienced, and it has a negative impact on behaviors, relationships, and health. The term “eustress” refers to positive stress that is associated with improved performance and productivity. “Distress” is negative stress that is associated with performance decrement and negative health consequences. The individual’s perception of the stressor and coping resources determine whether a situation is eustress or distress. College graduation is a stressor for most. The student who has a job or who has been accepted to a graduate program likely perceives the stress of graduation as eustress, whereas the student who has student loans and no immediate plans of a job or further education perceives distress.
If you’re operating in Alpha mode, you’ll feel very present and in the moment. You might be somewhat reactive to the world around you, but you’ll feel like you have time to process what’s going on rather than just react on instinct. This is a wonderful state to achieve when meditating or doing something that requires coordination, focus and learning.
The Frequency following response (FFR), also referred to as Frequency Following Potential (FFP), is a specific response to hearing sound and music, by which neural oscillations adjust their frequency to match the rhythm of auditory stimuli. The use of sound with intent to influence cortical brainwave frequency is called auditory driving,[39][40] by which frequency of neural oscillation is 'driven' to entrain with that of the rhythm of a sound source.[41][42]