The term assigned refers to the process whereby the writer, or seller, of an option is asked to fulfill their obligation under their contract. When assigned, an option writer has the obligation to either sell or buy the underlying asset at the agreed to price.
The right to exercise an option always rests with the holder or the investor taking the long position in the contract. While the holder of a call option has the right to buy the underlying commodity, the holder of a put can exercise their right to sell the underlying commodity. Investors that take a short position in an option are assigned when a holder exercises an option.
When a buyer exercises their option, a notice is sent to the seller of the contract as determined by the Options Clearing Corporation (OCC). When this occurs, the seller is said to be assigned; the process of assignment is random. When assigned, the writer of a put option is obligated to buy the security from the holder of the put at the agreed to price. In the same manner, when the writer of a call option is assigned, they are obligated to sell the security to the holder of the call option at the agreed to price.
American options provide the holder (or buyer of the option) with the right, but not an obligation, to exercise their option at any time before its expiration. However, the writer of an option has an obligation to sell or buy the underlying security if assigned. In practice, most options are never exercised by the holder and expire worthless or are eventually closed out.