The main purpose of Clan is for breeding. You can put in up to 15 cats to start with, any species you wish. Clans can also be Public or Private. Meaning, with Public anyone can freely join and add/remove their cats at will. With Private you have to approve each member along with the cats they request to join, you can edit the members so they can freely add feli. As well, there are Closed clans.
The clans tend to have a more positive influence on interactions, therefore increasing chances of baby felis.