"wax," late 15c., from French cire "wax" (12c.), from Latin cera "wax, wax seal, wax writing tablet," related to Greek kēros "beeswax," which is of unknown origin, perhaps a non-IE word. As a verb, "to wax, cover with wax" (cloth, for waterproofing), late 14c., from Latin cerare, from cera. Related: Cered.
"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.