In the Steam Marketplace, I've noticed some trading cards called "Foil Trading Cards". I can see from the price difference between an original and foil card that foil cards are much more valuable, but do foil cards actually do anything different than regular cards?
Steam Foil Trading cards can be crafted into foil badges, similar to how you can craft normal badges from normal trading cards. Other than that, it is useless, but everyone thinks they need one. They are essentially rarer trading cards. They are found the same way normal trading cards are.
From the Trading Cards FAQ:
What are Foil Trading Cards?
There is a small chance whenever you get a Trading Card from playing a game that it will have a special foil border. You'll need to collect a set of foil cards in order to craft them into a foil badge. There is no extra benefit to having foil cards or foil badges aside from their rarity.