Breathing is the one automatic system that will hand you the controls if you ask.
Your heart won't slow because you requested it. Digestion carries on regardless of your opinion. But breath will let you take it manually for a minute and then quietly take itself back, and the rest of you pays close attention to what you did while you had it.
That is the mechanism, and it is less mystical than it sounds. A long exhale is a message sent downward in a language much older than reasoning, to a part of you that was never going to be argued with.