Armory is the guild store where you can spend the Honor you received in guild battles and in Arenas.
To get to Armory just tap on the icon of the little tent at any screen in the guild menu or on the button "Armory" on the "My guild" screen.
In the Armory, you will see items available for you. Their availability depends on the amount of Honor you have, the level of your guild and your own rank in the guild.
The game will automatically open the whole list of items in the shop, but you can choose any tab you need (potions, ingredients, magic spheres, etc.)
Tap on any locked item in the shop, and you will see the amount of this item you have right now, and a little bit lower - the reason why this item is locked or an active button for purchase for Honor.