From the Super Mario Wiki
The Golden Card is an optional item in Super Paper Mario. Its purpose is to access the secret minigame Hammer Whacker at the Flipside Arcade. The Golden Card is found in a hidden room in the The Overthere in Flopside. Mario can access this room by flipping into 3-D and walking past the wall that is by Garson. Mario can then find the Golden Card (as well as a Cooking Disk) in a Treasure Chest. Once Mario consults The InterChet with his Golden Card, The InterChet says that the current player is a welcome gamer and makes Hammer Whacker available to him. It resembles the Gold Card from the prequel.