PvP challange doesn't need too many explanations. You will just digit the player you want to fight, and starts a battle. It is the only battle where two people face each other in real-time, and it is just for fun: there is no reward, nor golds neither carats, and you can do it as many times as you wish, if you find an opponent!
It is a really good way to learn to use your team! And for those players under level 6, could be usefull for a daily quest.