Hey, great question, though I'm not sure if you want the audio or neurological explanation, or both :)
I'm also not sure how technical you want or how much you know already, so apologies if I'm too technical, and apologies if I'm not technical enough. I'll just try to start from the beginning and lay everything out from there, as briefly as I can. Tragically, however, I was born without brevity.
1) Brain.fm: The Brain's Perspective
When a sound enters your ear, it's converted from a pressure wave to an electrical impulse, which you can measure in the brain as a kind of spike on an EEG, or a cortical response. If the sound plays again, another spike occurs (although typically smaller). If a sound keeps being repeated in a fast and precise enough way, the cortical responses start to resemble rhythms already in the brain.
For example, if you tap your finger rapidly on the table, you might be tapping at 10hz (10 taps a second). 10hz is also a very dominant in the brain. If you could tap your finger precisely enough, and for a long enough time, what you would see in the brain (if you know what you're doing) is new activity at 10hz. This is called the Frequency Following Response, and it's well established. Check it out on pubmed, etc, if you're interested.
Now if you keep tapping for even longer - and again, if you're super precise about it - your existing brainwave patterns near that same frequency will start to align themselves towards the phase and frequency of your tapping.
BTW sorry about the delay in responding to you. Believe it or not, in between some meetings I was searching for a good article this whole time to show you. Here it is: http://www.pnas.org/content/111/41/14935.full
This effect is called lots of things, including, confusingly, the frequency-following response by some in the private sector. It's most often known by the public as brainwave entrainment, but that's rarely in the literature. In the literature you see all kinds of words for it: neural entrainment, auditory driving, auditory entrainment, steady state responses of various types... The level of confusion over what to call this thing is only eclipsed by the number of names made up for methods to induce it - all referring to the same thing: rhythmic auditory stimuli. No, better not call it that, in this paper its gonna be sinusoidal amplitude modulation, click trains, acoustic iterance, isochronous auditory stimuli, temporal sound... So, it gets a bit crazy when you try to search for this stuff (so we'll be adding even more to our bibliography/research library soon. Let me know if you haven't seen that yet).
For the sake of this post let's just call it Entrainment.
Something that's also being figured out is how to define when exactly Frequency Following ends and Entrainment begins. Some say it doesn't matter, others say it's when the phase lines up, or if the new rhythm persists even when the external stimuli is removed, as in the article I linked you to. There's also ways to approximate the root source of a neural rhythm (external or internal), if you also feed the stimuli into the analysis at the same exact time.
Anyway, to sum it up, what we're doing is creating a rhythmic stimuli that resembles frequencies already in your brain. We play that stimuli long and consistently enough to actually register a pretty solid response on an EEG.
Of course, it gets more complicated than that. This is the brain we're talking about. The waveform of the audio modulations matters (brainwaves aren't perfect sine waves, after all), the way the frequency is changed over time matters. When do you take a break from the stimulation? When do you tone it down, or turn it up? And how do you adapt to people on an individual level? How do you measure it? Audio processing can change dramatically in the brain depending on the content of the audio!
But at any rate, changing the brainwaves of a person like this can also change their mental state. I'm not saying it takes over the brain. It just.. nudges it a bit in the right direction.
So that's the basic outline from that perspective. Hope it makes sense, of course if you have any questions don't hesitate.
2) Brain.fm: The Music Perspective
From an audio's point of view, we're doing a number of things to subtly create that necessary rhythmic stimulus.
a) We're modulating every piece of audio. It's these modulations that create a rapid rhythmic stimulus. If you listen carefully to Brain.fm, you may hear a fluttering sound. It's more obvious in some parts over others. We're using filtering techniques to target some frequency bands over others (and by frequency here, I'm now talking about the frequencies of pitch, not brainwaves, where a cello would be low and a violin would be high in frequency). Doing this, we can single out instruments, modulate parts of a nature soundscape but not others, or disguise the modulations as vibrator, tremolo, or the natural vibrations of instruments, strings or the LFOs of electronic music..
b) We align everything else in the session to the brain-frequency we're trying to hit, so there is no interference from a stray drum beat or a snapping twig. Not only is there no interference, but the entire audio "scene" is being actively used to guide your brain toward the goal state.
The 3D audio also factors into this a lot, because the mind pays attention to motion, and that helps elliminate habituation. But that's another story.
Hope this helped explain it. Completely understand if you need clarification, or an entirely new answer hah!
:)
- Adam from Brain.fm