- They are rare
- They have meta data that associates them with something we would consider "art". That could be a music file, movie, but is most often an image or a "card".
People buy and trade them either to collect them because they think they're cool or to "play" them if they're associated with a game. Some artists create extra incentives involved in owning their art - for example one I know keeps a locked playlist on Soundcloud that only people that own his token can listen to. In all cases, any assets you buy will end up in a "wallet" that you can think of like a trading card binder. This wallet is public, so anyone can see what you own and prove that you own it.
Rare Digital Art takes a lot of forms and is an exploding medium. Rare Art Labs (rareart.io) helps traditional artists make RDA, Spells of Genesis is a card game using RDA, Crypto Kitties is like tamagachis on the blockchain, Rare Pepe Wallet takes the "rare pepe meme" concept from Reddit and makes it real, etc.