They are obtained after you complete a dungeon. For each dungeon you complete, you will receive a box or loose card located in your Inventory. When you open the box, you will receive a card along with other random items that you can use.
It can be collected and serve to increase Attack Speed. Although this increase isn’t shown in your character’s stats, it is noticeable. Additionally, the cards can temporarily transform you into the monster on the card (the Monster Card buff is displayed next to the map).
Collect as many cards as you want and have fun transforming into some monsters!