Wild card is a Dungeoneering reward item. For 20,000 Dungeoneering reward tokens, it unlocks the ability to gain a random free card upon entering a Sinkhole. Despite the icon in the shop displaying a Beguiling Smoke Devil card, the card gained at the beginning of each sinkhole is completely random.
It is not possible to buy this unlock a second time, doing so will yield the message "You have already unlocked this perk."