Most often refers to the elusive and mythic advance offered an author for a work, usually of prose, or some variety of prose (memoir, novel, biography), involving large-print editions. Apparently the average advance is approximately $100,000 dollars, one third of that in Canada. This is approximately the cost of a good MFA program. Consider the ratio and payoff if you are considering such things. Historically the advance is not associated either with poetry or the avant garde, though perhaps a conceptual advance might be offered in the way of fame, or lineage. An advance might signify a fork in the road of one's literary aspirations. A litmus test of sorts. It might also be a concern to those without a trust fund or those who prefer to eat. There is or is not a relationship between advance and readership.
Other possible uses: advance reading copy, advance reviews, and to advance one's career. The latter may or may not involve stepping on heads and/or slaying the competition.