PvP means Player versus Player, these are solo or group battles (also known as rallies) against another player’s base or troops. 

IMPORTANT: Players are able to attack one another at any time. Activating a shield around your city is the only way to safeguard your city. Shields only protect the troops inside your city. Troops that are outside of your city can still be attacked, injured and killed.

There are Free for All and other PvP specific events mixed into the game schedule - in order to earn points and compete in these type of PvP events, you will have to attack and defend against other players.