They have the typically ordinary day-to-day of a Tokyo high schooler - attending class, after school activities and part-time jobs. But they also undertake fantastical adventures by using otherworldly powers to enter the hearts of people. Their power comes from the Persona, the Jungian concept of the "self".
The game's heroes realize that society forces people to wear masks to protect their inner vulnerabilities, and by literally ripping off their protective masks and confronting their inner selves do the heroes awaken their inner power, and use it to strive to help those in need.
Ultimately, the group of Phantom Thieves seeks to change their day-to-day world to match their perception and see through the masks modern-day society wears.