A Monster Card is a drop (loot) from a monster in the form of a green card. These cards can be worn in slots, unlocked every 10 levels.
The cards function to improve stats.
The Green PecoPeco Card applies the following, +3 Str, +3 Agi, +2 Wis, +3 Vit.
Some cards such as the Green PecoPeco and Pecopeco card also have a set bonus, while wearing the full set, you get an additional stat bonus.