A term usually arising with respect to copyrightable works such as songs, books, and scripts. It is typically an advance on royalties from the entity to which publication rights have been sold.
Advances may be recoupable or non-recoupable; where recoupable, the advance will be recouped (or repaid) from the royalties generated: If the royalties generated do not exceed the amount of the advance, the royalty account can be said to be un-recouped. If recoupable, when the work is published the advance will be deducted from royalties due at an agreed rate, possibly with interest or some other uplift.
Advances may be non-refundable or refundable. Typically, even a non-refundable advance only becomes non-refundable once the putative author has made certain efforts to deliver the contracted-for work. See Certainty/Uncertainty Trade-Off.
Whether an advance is recoupable and/or refundable may have significant tax consequences – a non-refundable, non-recoupable advance is essentially income to the recipient (taxable) and a cost to the publisher. A refundable, recoupable advance is a loan and thus an asset to the publisher and, unless forgiven, not income for the recipient.