When an option is in-the-money at expiration, meaning that the price of its underlying security is above the strike price for a call or below the strike price for a put, the option holder will likely exercise. For the option seller, when this happens it's possible they will be assigned. If a seller is assigned on a call they have sold, they are obligated to deliver the underlying. If they're assigned on a put they have sold, the seller is obligated to buy the underlying.
Any time an investor has a short position in an option, meaning they are the seller, the investor would have to be aware of assignment risk. However, certain strategies with multiple option positions can be used to offset this risk, at least in part. The Options Clearing Corporation (OCC), which clears listed equity options in the U.S., assigns exercise notices via an SEC-approved random assignment process.