The Armory is the guild store where you can spend the Honor you earned in Guild Battles and in Arenas.

To access the Armory, simply tap the little tent icon on any screen in the guild menu, or tap the "Armory" button on the "My guild" screen.
 

In the Armory, you will see the items available to 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 full list of items in the shop, but you can select any tab you need (potions, ingredients, magic spheres, etc.)

Tap on any locked item in the shop, and you will see the amount of that item you currently have, and a little bit lower - the reason why that item is locked, or an active button for purchase for Honor.