Items within World of Warcraft that are important because of 'non-combat' uses. Gear that looks good but has bad stats, items that you use for fun, etc.
Typically the term Vanity is used for Small Pets, however in this instance it is a blanket term meaning all things in game that would be desired for a reason other than its actual attributes. From an equip item that looks different or just an item with a name that means something to you, a Vanity item can be virtually anything.
On RP servers Vanity items are sometimes called Props.