mid-15c., "capable of being used to set fires," from Latin incendiarius "causing a fire," from incendium "a burning, a fire, conflagration," from incendere "set on fire, light up with fire, brighten," figuratively, "incite, rouse, excite, enrage," from in- "into, in, on, upon" (from PIE root *en "in") + candere "to shine, glow, be on fire" (from PIE root *kand- "to shine").
Figurative sense of "enflaming passions" is from 1610s in English. Meaning "relating to criminal burning" is from 1610s. Military use, of bombs, shells, etc., attested from 1871. The obsolete poetic verb incend is attested from c. 1500.