Guild vaults are a shared storage space that guilds can assign the ability to their members to add and/or remove items from.
Altdorf Guild Vault Edit
Inevitable City Guild Vault Edit
The guild vault within the Inevitable City is located in the bank south of the city near the healer.
Speak to the guild vault banker in the bank to access the guild vault. You can only view and withdraw items from the guild vault if your guild rank permits you to do so.