An adoptable is a character or creature design that you can buy. Once bought, the individual character/creature belongs to you and you are free to do whatever you want with it. Some people have original creature species that they created and have made adoptables for. They're not selling the ownership of the species, just a couple of individual designs. Every adoptable creator has their own set of rules to be followed regarding their adoptables, adpotable designs of individuals from an original species may have different rules to a random one off design.
Are characters you design and sell, you can just design the looks or even design the backstory and personality too. The person you sell them to has now all the right to use it and call that design theirs. (It is now their OCs, no longer yours)
People use this designs for roleplaying, I think they also use them for writing stories.