Out of breath or exhausted, or having been wound backward.
From 'back' plus 'winded' (having the wind knocked out of one's lungs). The term emerged in the 1800s as 'winded' became common in English.
Being 'backwinded' is actually physiologically interesting—when you're knocked backward suddenly, your diaphragm contracts unexpectedly, which is why getting the wind knocked out feels so alarming and why it passes quickly.
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