late 14c., fibre "a lobe of the liver," also "entrails," from Medieval Latin fibre, from Latin fibra "a fiber, filament; entrails," which is of uncertain origin, perhaps related to Latin filum "a thread, string" (from PIE root *gwhi- "thread, tendon") or to Latin findere "to split" (from PIE root *bheid- "to split").
Meaning "thread-like structure in animal bodies" is from c. 1600 (in plants, 1660s); hence figurative use in reference to force or toughness (1630s). As "textile material," 1827. Fiberboard is from 1897; Fiberglas is attested from 1937, U.S. registered trademark name; in generic use, with lower-case f- and double -s, by 1941. Fiber optics is from 1956.