The Cooking skill card is part of the skill cards Treasure Hunter promotion. After winning a prismatic skill card on Treasure Hunter, choosing Cooking will turn it into the cooking skill card, and grant you a skill card deck if you don't already have one. You have to gain Cooking experience equal to the amount granted by a medium XP lamp, to complete the card, and then it can be returned to your deck, and you can start on a new card. You can only have one skill card in progress at once, and you can only complete each skill card once.
The objective is to complete all 26 skill cards in your deck, which will grant you a large experience reward in any skill, with the amount dependent on your level, in the same way as Treasure Hunter lamps. You can only win prismatic skill cards from 29 August until 9 September, but you can continue to complete your previously won cards until 9 October. If you don't complete all of the cards, you can turn your incomplete deck in for a substantially smaller experience reward.