Avatar items are under the equipment tab in a box labeled Featured Items.

They are mostly bought with Favor Points, however you can get a basic outfit with mob Cash.

Each Avatar item has an attack, defense, spirited attack or defense percentage boost that will help you when you attack someone or when someone attacks you. You will see this on your avatar page in green below your avi.

To load the Avatar items buy them, then click on the Avatar tab, and click on each item category and you will see a list of available avatar items you can equip. If they have any bonuses it will show it in green under the item. Once you click on an item it is automatically applied and loaded. Your total loadout will be displayed in green.