Binaural beats don't quite work without headphones (unless you got a carefully positioned speaker setup, and even then the effect probably isn't optimal).

It's a psycho-acoustic effect of hearing a beat frequency when playing two slightly differently tuned sounds in each ear. It's like the regular beat frequency effect that you use for tuning a guitar, play a 440Hz and 442Hz tone simultaneously and you'll hear a 2Hz beating frequency because the soundwaves physically cancel out twice per second. The binaural trick is that you play one tone in the left ear and the other in the right ear. So the tones never physically meet, yet your brain hallucinates the corresponding beat frequency regardless. You can easily test this for yourself if you're handy with audio software (try two sine waves first--careful with the volume though, pure sine waves can carry a lot of energy in headphones). Your brain is doing some really cool signal processing :)

The other part is something called "brainwave synchronisation" or "entrainment". Parts of your brain pulse at a certain frequency between 3Hz and 12Hz or thereabouts. 12/10Hz is when you're active and awake, 3Hz corresponds to very deep sleep (I think of the dreamless kind, but it's been a while). The specific frequency ranges have names of Greek letters (12/10Hz = alpha/beta), but from what I can tell and given that it's super hard to measure, thinking about it as "active" to "less active" is just about as useful (IIRC think 8-10Hz is supposed to be more "creative" or something).

The idea being that you start a session at roughly your current brain frequency, so probably in the 10-12Hz "active" range. And then it slowly slides down to the desired relaxation frequency over the course of 10-30 minutes or so. Some programs have specific sequences, going up and down, probably inspired by sleep cycles switching between deep sleep and more active states. A full sleep cycle is about 4.5 hours and brainsync sessions are usually much shorter.

Now, the funny thing here is, that there is actually NO reason that you need binaural beats to do this brainwave synchronisation. It's two entirely unrelated phenomena (if I'm mistaken and they are somehow related, PLEASE comment or link me :) I'm fascinated by this stuff, even though sceptical). It always seemed to me they focused on binaural beats simply because it has this extra "woo factor" of being about frequencies that "aren't really there" (the hallucinated beat frequencies). There's another technique called "isochronic tones", which are just beeps or clicks repeating at the desired 3-12Hz frequency, that works just as well (or perhaps better because it is direct stimulation instead of being deduced in the brain).

Binaural beats have one advantage though, that isochronic tones are SUPER annoying to listen to. And with the proper DSP plugin, you can apply binaural beats over any existing audio track, with minimal artifacts or distortion. So it's just much more nicer to have this soothing ambient soundscape, that also happens to have binaural beats embedded in it.

Except the problem is, which really muddles my conclusion of "does this even work", most people I hear reporting about binaural beats, don't actually listen using headphones. They just play it on their sound system while sleeping, which are often two tiny speakers near eachother, on the other side of the room. They report it really helps them sleep. I'm 99.99% sure that they're just falling asleep because of the nice ambient soundtracks binaural beats are laid over. There's just no way the binaural beat effect carries accurately over a room from cheap speakers.