An expense, often referred to as a "recoupable" or "shared" expense, is a type of transaction that gets subtracted from the income to find the net of a release/track/etc.
The net is what is used to find the payee share (based on their split %), and so expenses are therefore considered "shared" between everyone participating in the net, according to their split %. In other words, if a payee has a 10% split on a release, they're also effectively shouldering 10% of the expense burden, if/when the release recoups its expenses.
Expenses are typically things like manufacturing, PR, freight, videos, and other production costs directly related to a particular release.
They typically do *not* include things considered "overhead," such as labor, rent, accounting and taxes. Very often what can be considered an expense vs. overhead is detailed in the contract between the catalog and the artist/payees.