early 12c., brennen, "be on fire, be consumed by fire; be inflamed with passion or desire, be ardent; destroy (something) with fire, expose to the action of fire, roast, broil, toast; burn (something) in cooking," of objects, "to shine, glitter, sparkle, glow like fire;" chiefly from Old Norse brenna "to burn, light," and also from two originally distinct Old English verbs: bærnan "to kindle" (transitive) and beornan "be on fire" (intransitive).
All these are from Proto-Germanic *brennanan (causative *brannjanan),source also of Middle Dutch bernen, Dutch branden, Old High German brinnan, German brennen, Gothic -brannjan "to set on fire;" but the ultimate etymology is uncertain. Related: Burned/burnt (see -ed); burning.
Figurative use (of passions, battle, etc.) was in Old English. The meaning "be hot, radiate heat" is from late 13c. The meaning "produce a burning sensation, sting" is from late 14c. The sense of "cheat, swindle, victimize" is attested from 1650s. In late 18c, slang, burned meant "infected with venereal disease."
To burn one's bridges(behind one) "behave so as to destroy any chance of returning to a status quo" (attested by 1892 in Mark Twain), perhaps ultimately is from reckless cavalry raids in the American Civil War. Of money, to burn a hole in (one's) pocket "affect a person with a desire to spend" from 1850.
Slavic languages have historically used different and unrelated words for the transitive and intransitive senses of "set fire to"/"be on fire:" for example Polish palić/gorzeć, Russian žeč'/gorel.
c. 1300, "act or operation of burning," from Old English bryne, from the same source as burn (v.). Until mid-16c. the usual spelling was brenne. Meaning "mark or injury made by burning" is from 1520s. Slow burn is attested by 1938, in reference to U.S. movie actor Edgar Kennedy (1890-1948), who made it his specialty.
also burnout, "drug user," by 1972, slang, from the verbal phrase, which is attested from 1590s in the sense "burn until fuel is exhausted;" see burn (v.) + out (adv.). The immediate source is perhaps the use of the phrase in reference to electrical circuits, "fuse or cease to function from overload" (1931). Also compare burnt out "extinct after entire consumption of fuel" (1837). The meaning "mental exhaustion from continuous effort" is from 1975.
late 13c., also as a surname, Brenner, "person who makes bricks," agent noun from burn (v.)). As a name for a part of a lamp where the flame issues, from 1790. Of the heating elements on gas cooking-stoves, by 1885.
"the husk of wheat, barley, etc., separated from the flour after grinding," c. 1300, from Old French bren "bran, scurf, scales, feces" (12c., Modern French bran), perhaps from Celtic and connected with Gaulish *brenno- "manure" (but OED is against this) or with burn (v.). The word also was used 16c. in English for "dandruff flakes."
Middle English brenning, from Old English, "scorching, hot;" mid-14c. in figurative sense of "powerful, strong, ardent;" present-participle adjective from burn (v.)). The meaning "causing excitement" is by 1865 and is the sense in burning question (1865), which matches French question brûlante, German brennende Frage. Burning bush is from Exodus iii.2. It was adopted as an emblem by Scottish Presbyterian churches in memory of the 17c. persecutions. Burning-glass is attested from 1560s.