early 12c., Nativite, "feast-day celebrating the birth of Christ, Christmas," from Old French nativité "birth, origin, descent; birthday; Christmas" (12c.), from Late Latin nativitatem (nominative nativitas) "birth," from Latin nativus "born, native" (see native (adj.)). Late Old English had nativiteð, from earlier Old French nativited. From late 14c. as "fact of being born; circumstances attending one's birth."
"cylindrical body of tallow, wax, etc., formed on a wick and used as a source of artificial light," Old English candel "lamp, lantern, candle," an early ecclesiastical borrowing from Latin candela "a light, torch, candle made of tallow or wax," from candere "to shine" (from PIE root *kand- "to shine").
The Latin word is also the source of French chandelle, Spanish candela, Irish coinneal, Welsh canwyll, Russian kandilo, Arabic qandil, etc. Candles were unknown in ancient Greece (where oil lamps sufficed), but common from early times among Romans and Etruscans. Candles on birthday cakes seem to have been originally a German custom.
To hold a candle to originally meant "to help in a subordinate capacity," from the notion of an assistant or apprentice holding a candle for light while the master works (compare Old English taporberend "acolyte"). To burn the candle at both ends "consume or waste prodigiously" is recorded from 1730.