But the question is: Does it have a special effect on the brain? A lot of people think so. The basic claim being made for binaural beats is "resonant entrainment". Entrainment, in physics, is when two systems which oscillate at different frequencies independently are brought together, they synchronize with one another, at whatever the combined system's resonant frequency is. Examples of entrainment occur in animals in nature; for example the chirping of crickets or the croaking of frogs. Synchronization of menstrual cycles in women is another example. Even people coming together and dancing with one another is a type of entrainment. The basic claim for binaural beats is that the perceived low-frequency beat will entrain your brain wave pattern, thus forcing your brain into some desired state.
I am very encouraged by my stroke recovery progress after starting with Sacred Acoustics! I have been listening to the extended Light Body (non verbal) recording almost constantly. I keep it on the repeat mode and at a low enough volume so that I do fine with ordinary conversation as I go about my daily activity. The results with constant listening of Light Body are so fantastic, I hate to stop! 
In addition to potentially boosting sleep-promoting hormones, binaural beats may also reduce our perceptions of pain. A 2017 study found binaural beats used in combination with visual stimulation led to reductions in patients’ perception of acute pain. Other recent research showed binaural beats helped improve pain perception in patients with chronic pain.
... Audio visual stimulation effects people on two levels: Budzynski (2001) reports significant improvement of mental capabilities after AVS in 75-year old male. Cruceanu and Rotarescu (2013) proved that the exposure to 30-minutes of audio-visual stimulation with the frequency of 10,2 Hz significantly improves cognitive skills. Based on their research, authors claim that people need to be exposed to AVS at least for 20 minutes in order to achieve positive effects. ...
“Stress” is a commonly used term, and it is often used with different meanings. The standard definition for stress that will be used in this article is the disruption of the body’s homeostasis or a state of disharmony in response to a real or perceived threat or challenge (8). The threatening or challenging situation is referred to as a “stressor.” When a person encounters a stressor, the body prepares to respond to the challenge or threat. The autonomic nervous and endocrine systems respond by producing the hormones epinephrine, norepinephrine, and cortisol. The result of this hormone production is a cascade of physiological reactions that make up the stress response. Epinephrine and norepinephrine are involved in the initial changes that take place to prepare the body to react and to prepare for a challenge. These responses include increases in heart and respiration rates, blood pressure, perspiration, and energy production (8). There also is a suppression of immune function, production of β-endorphin (the body’s natural pain killer), and increased acuity of the senses. These changes make up the fight-or-flight response, which prepares the body to cope with the stressor. If the stressor is perceived as negative or more as a threat than as a challenge, cortisol production is increased. Cortisol is involved in energy production but also suppresses immune function.
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.

Entrainment is a term originally derived from complex systems theory, and denotes the way that two or more independent, autonomous oscillators with differing rhythms or frequencies, when situated in a context and at a proximity where they can interact for long enough, influence each other mutually, to a degree dependent on coupling force, such that they adjust until both oscillate with the same frequency. Examples include the mechanical entrainment or cyclic synchronization of two electric clothes dryers placed in close proximity, and the biological entrainment evident in the synchronized illumination of fireflies.[13]