Wizarding Challenges are collaborative pursuits where you and other wizards can battle against Foes to earn rewards. Fortresses are in-game locations at which Wizarding Challenges take place.
You can play Wizarding Challenges solo, but for a better chance at defeating difficult Foes you can battle with up to 5 players in a group. When you play with other players, you can also earn a larger reward. Fortresses with active players in a Wizarding Challenge appear on the Map surrounded by a green aura. Look for these Fortresses on the Map to battle with other wizards.