the.com/sweatband

means A band of absorbent fabric worn around the wrist or forehead to soak up sweat during exercise.

from Straightforward compound of 'sweat' and 'band' — a plainly descriptive coinage from the 20th century, born alongside the rise of organized sports and gym culture, when terrycloth and similar absorbent fabrics became cheap and common enough to wrap around a head or wrist. No hidden story here: the word does exactly what it says, which is rarer in English than you'd think.