The art you see on our site are each backed by a unique token that lives on the blockchain. This token is signed by the artist and links directly to the original piece. By linking an artist's work to a token, this ensures authenticity and a clear record of ownership.
When purchasing a piece of art you become the owner as one would with any physical piece of art. Some purchase purely for speculation -- if you happen to own an early piece by an artist that becomes popular you could find that the value appreciates. Others purchase as a way to show their support for the artist or the work itself. Everyone can see your collection (even using other sites!) as it is open data on the blockchain.
Lastly, with Async there is the special ability to alter Layers. Layers have unique parameters (set by the Artist) in which they influence the overall Master image. Only the Layer owner has permissions to push the change and everyone will see when they submit it.