What it means
Party-party costs (now often called "ordinary" or "standard" costs) are the costs one party can recover from another under a costs order. They cover costs reasonably incurred for the conduct of the litigation, but typically well short of what the successful party actually paid their own lawyers (often loosely estimated at around two-thirds). The shortfall is borne by the winning party, unless the court orders the higher indemnity basis, for example to mark disapproval of conduct.
How it's used
Even after winning, she recovered only party-party costs, leaving a gap between that and her full legal bill.