The scientific explanation :

The researchers identified a small group of neurons located at the base of the brainstem that provide the link between breathing and relaxation. A small "cluster" in the middle of a larger group of neurons, believed to be the center of "breath stimulation" (like cardiac stimulation).

Inspiration and expiration profoundly stimulate this small "group" of neurons, which in turn transmits signals to another region of the brainstem, the locus coeruleus. If the latter is very stimulated, it triggers, via other parts of the brain, anxiety and stress; on the contrary, if it is not very active, it leads to relaxation and calm. Now the locus coeruleus works in rhythm, and its tempo is set to... the breath. By blowing a big blow, the tempo slows down, this zone activates zones related to relaxation. And thus releases, in a way, "positive waves"...