How Asana (or movement practice) is described or defined in the the Yoga Sutras of Patanjali

Asana is the third limb of the eight limbs and is "not an end or a goal unto itself," "meditative practice is" (Bryant 2015, p. 283 + 284). "Less than one percent of the text occupies itself with asana" (Bryant 2015, p. 283).

The point is that yogic postures are useful only to the extent to which they facilitate fixing the mind completely.

~ Bryant (2015, p. 284)

Why was asana offered to yoga students as a physical practice?
Asana is conducive to a meditative practice. Postures and movement practice helps to absorb citta and still vrittis. The very first line of Patanjali's Yoga Sutras is "yogas citta-vritti-nirodhah" - yoga is the stilling of the fluctuations (vritti) of consciousness (citta).

Bryant, E. F. (2015). The yoga sutras of Patanjali: A new edition, translation, and commentary. North Point Press.