It is pretty much art people make and put up for adoption. By adoption, they mean someone pays to have the rights to that pet. TECHNICALLY, they do not own the pet and it does not become a part of a collection or anything. The person who bought the adoptable just has the right to make more art of the adoptable or go around calling it their own (as long as they say they bought it from the original artist, of course). I was super confused about this before too... Put simply, an adoptable is a pet that an artist designs and draws that another person can buy.
Another thing to not is that sometimes artists will put a large watermark over the adoptable. Once someone buys it, they will send the picture of the pet without the watermark to the new owner. That way it prevents people from stealing the art.
Hope this answers your question!