For pm-settlement products it is usually the official closing value. For am-settlement products it is a special opening quotation built from component opening prints. Either way it is an official figure, and disputes are settled against it, not against your platform's last tick.
Knowing which one applies tells you when your risk actually ends. Until the settlement value is struck, the position is live.
Example: your broker's chart shows an index low of 4,996 on expiration Friday morning. The published settlement value is 4,991 because several large components opened lower before recovering. A 4,995 put you believed was worthless settles at $4.00, or $400 per contract.
Related: am-settlement, pm-settlement, cash-settled-option, index-option