A Clan is a community of players who join forces so they can communicate with each other, test setups in friendly fights and participate in the upcoming Clan battles.
A clan can be found by tapping on the icon in the main menu. You can find a particular Clan using a search function or create your own Clan in "Clans". There can be up to 50 players in one Clan. Creating the Clan costs 1000 Coins and you have at least level 5 to create a new Clan.