A three-way match compares three documents before a supplier invoice is paid: the purchase order (what you agreed to buy, at what price), the receiving record (what actually arrived) and the invoice (what the supplier is billing). If they agree within a tolerance, the bill is approved; if not, someone investigates.
For food distributors the match catches short shipments, substitutions, damaged cases and price changes the buyer never agreed to. Without it, you pay for what was ordered rather than what arrived.
In APFoodz a bill that does not match goes to an approver before it is paid.