I'm looking through my copy of Legends of Anglerre for this, and also searched the Spirit of the Century SRD, and I'm completely stumped as to exactly what an "advance" is. In both instances the terms are used out of the blue without any prior explanation of what they are or any entry in the index, nor is there a glossary of terms (something I'd have never guessed I would miss).
In SOTC, advances are bonuses to NPC's (Ch5, p78, heading Companions), and are spent when the NPC is created. An advance can...
LoA uses the same basic mechanics; rules for advances are on page 166-167.
In both, they are defined for companions, but are also used for contacts and some other types of NPC's.
SOTC vehicles have other advances, doing different things, but still are changes made based upon stunts possessed to something other than the character with the stunt.
With the GM's and group's permissions, you might be allowed to leave some unspent, and spend them as certain elements are found to be needed.