The Avatar Inventory is a storage for avatar items so one does not need to hold them in their inventory. It is per character; to transfer avatar items to other characters on the same account, use the cloak room. The Avatar Inventory holds up to 150 items.
To access the Avatar Inventory select Equipment/Status from the Main Menu or click the Equipment/Status Icon at the bottom of the screen(B is default shortcut). Click on the tab labeled "Equip". Click "Change Display" to toggle between equipment and avatar items. Click the Avatar Inventory icon on the right side of the avatar display. This will open the Avatar Inventory window.
Equip an item by either double clicking on the item in your inventory or dragging the item onto the slot on the avatar display page. Unequip an item by double clicking it.
Make sure to check your Avatar Inventory before deciding to delete your character.