Trading in the option stops on the third Friday, but the option owner has the ability to exercise the option on the third Saturday, the day after expiration. Many contracts have a quarterly expiration cycle; this convention is done in order to generate increased volume and associated liquidity in the contract.
For options on futures contracts, the expiration date may be different because the expiration does not necessarily coincide with the delivery month identified in the option contract. In certain instances, the expiration date for a future option may occur previous to the delivery month of a futures contract by a few weeks.
Several times per year equity options, equity index options, and equity index futures expire on the same date. These Fridays have become known as triple-witching days; the period before this expiration is typically marked by heavy trading in the contracts.