Brainwaves, or neural oscillations, share the fundamental constituents with acoustic and optical waves, including frequency, amplitude and periodicity. Consequently, Huygens' discovery precipitated inquiry into whether or not the synchronous electrical activity of cortical neural ensembles might not only alter in response to external acoustic or optical stimuli but also entrain or synchronize their frequency to that of a specific stimulus.
Some people believe that using this stuff can be a replacement for meditation. While sitting passively and listening to something that can give you the same effect frequency-wise as meditation, there is still far more benefit to meditating than just entrainment. Meditation and mindfulness allow you to really understand yourself on a level far deeper than technology will bring you.
Beta brainwaves are typically those we experience when we are wide awake and full of energy. You can think of this frequency as the equivalent of taking stimulants like caffeine, Adderall, or various nootropics. The Beta frequency is good for generating a concentrated, focused, and analytical mind. In fact, the brainwave you probably possess while reading this is of the Beta frequency.
Both brainwave entrainment and neurofeedback deal with brainwaves, but the similarity stops there. Entrainment pushes your whole brain into a pre-determined state, while neurofeedback teaches you how to move specific parts of your brain on your own. It is the differeence between forcing the brain into a given position, and skills building so you can move it there yourself.