When you make a purchase of 1100 Gran or more from the Cashier tab, along with your Gran your account will be upgraded with Premium Features at no additional cost. The Premium Features include double the number of slots you have for Card Files under the FILE menu from 10 to 20. They also include extra space in your in-game mail(double) and additional theater functionality, which allows you to watch Replays of your battles, and share them.
All users get a Free Trial of the Theater Tab. Whenever you finish a battle, you will be given the option to Save a Replay of that battle and start your Trial Membership. This free membership will last for one week.