I've been practicing mindfulness of breath (Anapanasati) lately and noticed this phenomena. During the initial few minutes, the breathing is generally short, but as the mind starts concentrating and gets still, the breathing becomes slower and slower. In fact, some times, I feel like one in/outer breath is taking like minutes. What actually causes this phenomena?
At least two things cause this phenomena: (1) the mind not desiring & not thinking, which results in the restless energy of desire & thinking not making the breathing restless & agitated; and (2) what Buddhism calls the 'Nirvana element' ('nirodha dhatu'), i.e., what science calls 'homeostasis', which, like the force of 'gravity', moves the breath towards the equilibrium or peace/stillness of Nirvana.
Whenever the mind is free from craving, clinging & desiring, the mind & the breath will enter into the 'stream' to Nirvana. It is the same as when a drug addict enters into 'cold turkey'. Natural forces purge the body of the drug addict of its toxins. Similarly, the 'cold turkey' of meditation dissolves the agitations of conditioned mental formations stored in the mind, body & breath, making the breath more calm & pure.
Your breathing is normally an autonomic function. Controlled by your brain and generally involuntary. That way we can sleep at night and not die.
But when we actually focus on it we take over that function. So what was a rate previously controlled by the brain automatically now becomes a rate we have more control over.
Of course what's being controlled is the amount of oxygen getting to the blood and the brain. It doesn't take much of a variance in that percentage of oxygen in the body to change how we feel - be it sluggish or excited. Our body automatically keeps us a little "hopped up" on oxygen so we have a little reserve to flee in case a sabretooth tiger approaches. When WE take over the breathing we tend to be more relaxed about it and lower that oxygen percentage a bit which increases the CO2 level and further relaxes our body.
This is why anapanasati meditation is so simple and so effective. It works right along with our body in relaxing.
Breathing is connected to your three centers - mind, body and heart. Watching breathing slows down breathing a bit which slows down thoughts/emotions. As a result your senses cool down. Your mind, body, and heart are in perfect balance which further slows down your breathing. This virtuous cycle results in stopping of breath which culminates in nirbana. You are no longer connected to your mind, body and heart. You have gone beyond your senses.