Aurum (abbreviated "AUR") is a virtual currency used in EVE to purchase items from the New Eden Store (NES). These items include cosmetic ship skins, clothing for your capsuleer, and skill extractors. AUR appears as a separate balance item (separate from ISK) in your character's in-game wallet and cannot be transferred from one character's wallet to another character, even if those characters reside on the same account.
Aurum can be acquired by converting PLEX into AUR (at a rate of 3500 AUR per PLEX), or by purchasing and converting Aurum Tokens. Note that Aurum cannot be converted back into PLEX.
How do AUR tokens work?
When you purchase an AUR package (with real-world money) you get the value of the package in Aurum Tokens. These tokens can be redeemed via the in-game redeeming system to any character on the account. From there, Aurum Tokens are an in-game item, much like PLEX, and can be moved and traded like any other such item. Once obtained, you can right-click and select "Redeem for AUR" in order to convert their value into AUR to be spent in the New Eden Store. After tokens have been redeemed, AUR is non-transferable.