The same information as the site, plus features to automatically track and manage your game progress:
Dungeon tracker - track dungeon completion status and unclaimed rewards
Drop tracker - show what you'll get when you finish the current battle
Record Materia tracker - to help you see which RMs you have unlocked but not yet acquired, what you have to to do get the best RMs, and which RMs are cluttering up your inventory and should be stashed
Score tracker - view all your Cardia progress and magicite completion times on a single page to help you see where to focus next
Soul breaks and legend materia - view all of the soul breaks, limit breaks, and legend materia that you own in a convenient two-column format
Relic draws - including currently open relic draws, unused Wondrous Draw and Acolyte Archive selections, percent chances, and soul break / legend materia details. Dupes are tracked within each banner to help you visualize the chances of a good draw, and a relic draw simulator lets you try your virtual luck.
Game options - optionally hide Roaming Warrior accolades for a cleaner UI