This is not your average RPG game. This takes place in Tokyo where your family allows you to take probation in school, outside Sojiro Sakura coffee and curry restaurant. You may be a silent protagonist, but your adventure is not an ordinary one at best. In summary, you'll encounter lots of hardships while also dealing with the distorted parallel world where people's evil desires overcame what's used to be the good side of the people. You'll slowly gain friends, learn to handle Shujin Academy and overcome people's evil hearts.
Anyway, let's break it down what you're going to do in this game: You'll do some platforming, doing turn-based role-playing battles, what's the right answer and how to raise up your stats between school and free time. But this is only exclusive to PlayStation 3 and 4 only. Go to the "Royal" section to learn more about additional features and what to expect that's exclusive to all current consoles.
Lastly, if you want to understand the story side, why not watch "Persona 5 The Animation" as a condense version of the game to learn as they're almost parallel to each other. Plus, it's easier to understand that way when you're not playing on console or PC.