Everything you've bought or received in the Mall lands in your Inventory. For cosmetic items like avatar skins, profile pictures, and banners, you'll see an Equip button — tap it to make that item active, and Unequip to switch back. Only one of each type can be equipped at a time.
Consumables, like XP boosters, work a little differently — instead of an equip toggle, they show as a quantity (for example, "×3") since they're meant to be used up rather than worn. Items also carry a rarity tier, so rarer finds are easy to spot at a glance in your collection.