This new feature will free a lot of inventory space, because you will be able to store your costumes, pets, emotes and mounts into an inventory, made specially for them! For every completed collection, you can get nice rewards, such as lockpicks, essences, AND - new "Upgrade" for your mounts!
When you click an emote/costume/mount/pet, it will give you a preview.
If you have any of these things in your inventory, you can simply click the green "+" icon displayed next to it, and it will be transferred to the Bag. This doesn't cost anything, and probably never will. You can click it with your RMB, and you can use it as if it was in your inventory.