12c., combination of Old Norse brenna "to burn, light," and two originally distinct Old English verbs: bærnan "to kindle" (transitive) and beornan "to be on fire" (intransitive), all from Proto-Germanic *brennan/*branajan (cf. Middle Dutch bernen, Dutch branden, Old High German brinnan, German brennen, Gothic -brannjan "to set on fire"). This perhaps is from PIE *gwher- "to heat, warm" (see warm (adj.)), or from PIE *bhre-n-u, from root *bhreue- "to boil forth, well up" (see brew (v.)). Related: Burned/burnt (see -ed); burning.
Figuratively (of passions, battle, etc.) in Old English. Meaning "cheat, swindle, victimize" is first attested 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. Slavic languages have historically used different and unrelated words for the transitive and intransitive senses of "set fire to"/"be on fire:" cf. Polish palić/gorzeć, Russian žeč'/gorel.