When you sell an option you now have the obligation to sell or purchase stock. You have or may not have to fulfill that obligation. If you bought a call or put you would lose the premium you paid for the option plus whatever commissions and fees incurred on that transaction. You can anticipate being assigned any time your option becomes in the money. American-style is an option contract that can be exercised at any time between the date of purchase and the expiration date.
All stock options are American-style.
European-style is an option contract that can only be exercised on the expiration date. If Friday is a holiday, the last trading day will be the preceding Thursday. The last full day of trading for Equities and OEX is the 3rd Friday of the month. They settle on the close. The last full day of trading for SPX is the Thursday before the 3rd Friday of the month.