Traditional monthly index options settle to a value built from the opening prints of every component. Those prints do not all happen at the same instant, and the resulting number can differ noticeably from both the previous close and the level shown when the market opens.
Practically, it means the last day you can trade an AM-settled contract is the Thursday, and you carry the position overnight into a price you cannot see or hedge against.
Example: an index closes Thursday at 5,000. Friday's exercise-settlement-value prints 5,043, above every level the index visibly traded on Friday morning. A 5,025 call you thought would expire worthless settles for (5,043 − 5,025) × 100 = $1,800 against you.
Related: pm-settlement, exercise-settlement-value, index-option, triple-witching