I took Joel’s course some time ago, before he had thought of internal triggers, so I didn’t know what you were talking about. However, once you sign up for one of his courses, you continue to have access to it as long as it exists, so I dug up my password for the course and lo and behold I could still get in, and I viewed the new section on internal triggers.
The purpose of a bow trigger is the same purpose as squeezing a rifle trigger: you don’t want to know exactly when the shot will go off, or you will anticipate the shot and flinch or do something else involuntarily to screw up the shot. This is true whether there is a bang and a recoil, like a rifle, or just a release of tension, like a bow shot.
Joel has been trying all kinds of triggers over the years to find one that won’t disturb the shot just by using it. For example, I tried his grip sear, where you slide your thumbnail off some surface on your riser, and I was always annoyed by having to move my thumb while I was at full draw, and I guess he wasn’t totally happy with it either.
Anyway, he found that by squishing air around in his mouth, he could cause a sound that he couldn’t anticipate that he could use for a trigger, with less disturbance to the shot than a grip sear or other things he has tried over the years. Basically, it’s just building up air pressure inside your mouth until some of the air escapes through your teeth and makes a sound. How you do it is up to you. I tried it and it works. Whether I’ll ever use it or not to trigger the bow is doubtful, but you never know.