Honor is a currency that you can earn by participating in Guild Battles and Arenas.
The place where you can spend your accumulated Honor is the guild Armory. To open Armory, simply tap the little tent icon at any screen in the guild menu, or tap the "Armory" button on the "My guild" screen.
Please note that if you leave or are kicked out of a guild, you will lose all of your accumulated Honor within 5 hours. You will also lose your Honor if you switch guilds.