If this were Minecraft, a vault would be the same thing as a chest. The only difference is you can’t store as much stuff in it. Vaults are a way for you to take some stuff out of your inventory without having to destroy or discard the items.
You can build many vaults and each one can store 6 stacks of items. So you can technically store thousands of items in a vault, but there can only be six unique item types.
The greatest part about vaults is that they are linked to your inventory. If you transfer all of your ore over to a vault, next time you pick up some ore, it will go to the vault and not your inventory. When you want to convert some ore into a gold bar, the ore will be taken from the vault. This saves you having to go back and forth to get the items you need for crafting.
Is vault worth it?
Yes, absolutely. Your inventory is not that large in this game. Even if you are purchasing bag upgrades as often as possible, you will always find you are stuck for space. There are far more items in this game than inventory slots. I would advise you set aside an area and use it to build multiple vaults. Keep this as your storage area.