A somewhat formal or literary term for breathing or breath. In everyday speech, 呼吸 (こきゅう) is more common.
His breathing was rough and seemed painful.
He is gasping for breath and seems about to fade away.
gasping for breath; at one's last gasp; on the brink of death
Compound of 気 (き, 'spirit, air') and 息 (そく, 'breath'). The exact historical derivation is uncertain, but the combination naturally conveys the concept of breathing.