mid-13c., from Old French torche "torch," also "handful of straw" (for wiping or cleaning, hence French torcher "to wipe, wipe down"), originally "twisted thing," then "torch formed of twisted tow dipped in wax," probably from Vulgar Latin *torca, alteration of Late Latin torqua, from Latin torquere "to twist" (from PIE root *terkw- "to twist").
In Britain, also applied to the battery-driven version (in U.S., a flashlight). To pass the torch is an ancient metaphor from the Greek torch-races (lampadedromia) where the goal was to reach the finish line with the torch still burning. Torch-bearer "leader of a cause" is from 1530s. Torch song is 1927 ("My Melancholy Baby," performed by Tommy Lyman, is said to have been the first so called), from carry a torch "suffer an unrequited love" (also 1927), Broadway slang, but the sense is obscure.