With cards you can unlock certain decorations in your building menu, which you can open inside every location.
You always need to build the current decoration to move on to the next decoration.
You can have more than one card of a type, the amount of your cards is displayed with a number inside the little card star.
By using cards, you can earn stars and thus increase your player level.
You can obtain cards by playing the slot machine.
Go get 'em!