mid-13c., avauncen (transitive), "improve (something), further the development of," from Old French avancir, avancier "move forward, go forward, set forward" (12c., Modern French avancer), from Vulgar Latin *abanteare (source of Italian avanzare, Spanish avanzar), from Late Latin abante "from before," composed of ab "from" (see ab-) + ante "before, in front of, against" (from PIE root *ant- "front, forehead"). Compare avant.
The unetymological -d- was inserted 16c. on mistaken notion that initial syllable was from Latin ad-. From c. 1300 as "to promote, raise to a higher rank." Intransitive sense "move forward, move further in front" is mid-14c.; transitive sense "bring forward in place, move (something) forward" is from c. 1500. Meaning "to give (money, etc.) before it is legally due" is first attested 1670s. Related: Advanced; advancing. The adjective (in advance warning, etc.) is recorded from 1843.