Costumes belong to the so-called "Collectibles". These are items that have no physical in-game object, but can be activated either from the Collectible menu, or the Quickslot menu. They can be unlocked by either getting in-game achievements, or through purchasing them via Crowns, Crown Gems or Seals of Endeavors.
Full list of all "Costumes" that are available in ESO (Elder Scrolls Online). Costumes are added to your collection and are unlocked for all characters on your account. Costumes will override your character's attire visuals.