1908 as a political term, "an easing of hostility or tensions between countries," a borrowing of French détente "loosening, slackening" (used in the Middle Ages for the catch of a crossbow), from Vulgar Latin detendita, fem. past participle of Latin detendere "loosen, release," from de "from, away" (see de-) + tendere "stretch," from PIE root *ten- "to stretch." The reference is to a "relaxing" in a political situation.
Treated as a French word in English until mid-20c. The French word was earlier borrowed as detent (1680s) "catch which regulates the strike in a clock" (a French extended use of the word in its secondary sense "catch of a crossbow," which releases the tension in the string and discharges the bolt).