Assignment
The notice that obligates an option seller to fulfill the contract after exercise. Equity options settle in shares; cash-settled index options settle in cash.
Assignment is the other side of exercise. When a holder exercises, the Options Clearing Corporation assigns the exercise to a clearing member, which allocates it to one of its customers who is short the same series. A short call holder must then sell 100 shares per contract at the strike, and a short put holder must buy them.
American-style options can be assigned on any business day, so a short option can be assigned before expiration. Early assignment is more common around ex-dividend dates and when an option is deep in the money.
Illustrative example (hypothetical numbers, not a real trade): a seller of one $30 put collected $1.00, or $100. The stock falls to $26 and the put is assigned. The seller buys 100 shares at $30 for $3,000 while they trade at $2,600, a $400 difference that the $100 collected partly offsets.