Nadi
nāḍīThe body's energy channels. Ida, pingala, and sushumna come up whenever alternate-nostril breathing is taught.
The Hatha Yoga Pradipika is frank about why breath work matters: the channels are blocked, and practice clears them:
The breath does not pass through the middle channel (suṣumnâ), owing to the impurities of the nâdîs. How can then success be attained, and how can there be the unmanî avasthâ.
The original Sanskrit
malākalāsu nāḍīṣu māruto naiva madhyagaḥ / kathaṃ syād unmanībhāvaḥ kārya-siddhiḥ kathaṃ bhavet
Therefore, Prâṇâyâma should be performed daily with sâtwika buddhi (intellect free from raja and tama or activity and sloth), in order to drive out the impurities of the suṣumnâ.
The original Sanskrit
prāṇāyāmaṃ tataḥ kuryān nityaṃ sāttvikayā dhiyā / yathā suṣumṇā-nāḍīsthā malāḥ śuddhiṃ prayānti ca
Purify the channels so breath can enter the central one. That is the stated engineering behind pranayama in this tradition, in the text's own words.