Think of the payoff diagram for buying calls or puts – flip it upside down and that’s the payoff for selling.
You’re receiving the option premium rather than paying it and your max upside is the premium.
edit: regarding expiry – if they expire and the option isn’t exercised by the buyer, then you keep the premium and nothing else happens. If it expires and the option is exercised, then you deliver the asset and receive the premium.
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