Some random, maybe useful info. The mouthpiece works by preventing the jaw from recessing back. From my pre-purchase research I found out there are 2 main causes for snoring, this works for one of them.
Before the first use you put the mouthpiece into very hot water, bite it with jaw going forward, then let it cool down. You can reshape it the same way later in case the fit is not good enough. This was the case with me - I was waking up with a totally sore jaw (too much forward shift). After the reshape it is much better.
People report it is possible to make it possible to breathe through the mouthpiece. I found it unnecessary - maybe it even improves the airflow through the nose (I am not sure - could be placebo).
Googleable keywords is "mandibular advancement device". Good luck.
This is awesome info. My dentist was already recommending a dental guard since I apparently grind when I sleep - but those are crazy expensive compared to what I'm seeing elsewhere now.