The Yogasutra defines pranayama as stopping the breath: after a deep exhale, after a deep inhale, and after a normal breath. The hatha yoga texts specify different techniques of manipulating the breath, and the physiological effects of those techniques.
While the Yogasutra is concerned more with the mind, and hatha yoga apparently with the body, their goals are synchronous. Both pathways aim to quiet the mind. We all know that calming the breath will calm the mind.
But there is much more to traditional pranayama.
Pranayama is one of the limbs of classical yoga, the fourth among eight. Literally, the practice of pranayama is to lengthen the breath, and to stop the breath.
On one hand, the techniques of pranayama can be linked to the doshas of ayurveda—be classified as heating and cooling pranayamas. This is a way to use pranayama therapeutically.
On the other hand, deepening one’s experience of pranayama serves as an entry point to the experience of what is sometimes called the “subtle body” or “energy body.” That is, by practicing pranayama, interoceptive awareness of the body grows more refined and clear over time, allowing us to sense within us layers of body experience and mind-body connection that were inaccessible in our awareness earlier. This notion forms the foundation of the system of prana, nadis, and cakras, the part of yoga that is sometimes termed as “yoga physiology.”
Thus the heart of pranayama is the connection between mind and body that is explored using the breath. The entry to this practice is through cultivating a stable and comfortable awareness of inner body sensation in asana itself. We then deepen the practice in pranayama by finding greater absorption in that inner body awareness using the breath as a support and conduit.