Pranayama
prāṇāyāmaThe breathing practices: box breath, alternate-nostril, or simply "notice your breath." The fourth limb.
In the Yoga Sutras, breath work begins only once posture is settled, and it is defined as a kind of deliberate interruption:
Once posture is settled, breath regulation follows: attending to the flow of breath in and out, and gently slowing it.
“When there is this [stability of posture], the restraint of breath cutting off the flow of inspiration and expiration [follows].”
The original Sanskrit
tasmin sati śvāsapraśvāsayor gativicchedaḥ prāṇāyāmaḥ
The Hatha Yoga Pradipika states the reason to bother more bluntly than any modern teacher could:
The core claim of haṭha yoga: breath and mind are coupled. Disturb one and the other shakes; steady one and the other settles. So: work on the breath.
“Respiration being disturbed, the mind becomes disturbed. By restraining respiration, the Yogî gets steadiness of mind”
The original Sanskrit
cale vāte calaṃ cittaṃ niścale niścalaṃ bhavet / yogī sthāṇutvam āpnoti tato vāyuṃ nirodhayet
A disturbed breath disturbs the mind; a restrained breath steadies it. That single claim is why breath sits at the center of nearly everything on this site.