As long as it's in your inventory, everything you buy from the Main Shops will be 20% off. What will happen is when you successfully buy something, at the 'You've Bought' page, it'll say 'I see you have a discount card in your inventory, blah, blah, and you'll get the item for 20% less then the price you entered.

It stays in your inventory and for every item you restock it will lower the price by 20% (after you bought it). You can see how much in total you have saved under your Preferences. It works until you remove it from your inventory, so it's best to lock it in there.