Refers to the act of breathing heavily or being out of breath, often from exertion or excitement. Commonly used in the compound verb 息急き切る (to pant heavily).
Alternate spelling using kana for the second element; less common but still used.
Etymology
Compound of 息 (breath) and 急き (from 急く, to hurry or be impatient), literally 'hurried breath'. The exact historical derivation is uncertain, but the spelling is conventionally associated with the meaning of panting.