so what do you do in it?
It depends based on the game, but in Persona 4, here's the rundown.
You are a Japanese high school student who has to move to the countryside to live with his uncle because your parents are traveling. You spend an entire school year in tiny town called Inaba. Not long after your arrival, a string of murders breaks out in the town in a very public way. At the same time, there's rumors of a 'Midnight Channel' where you if watch on a rainy day at midnight, someone will appear on the screen.
After while, you realize that the people who appear on the screen turn out to be found dead shortly after.
At this point it turns into a murder mystery. You have an incredible amount of freedom though. You go through literal days of school. You have hang out with friends (referred to as Social Links), work part-time, study, eat, fish, play sports, etc. Each of these choices is beneficial to your character not only for story and character development but they tie Social Links to your Personas which are used to fight.
If you level up your Magician Social Link (one of your best friends in the game), you're able to create more powerful personas of that type and when you do, you get bonuses. It's all tied together.
Lastly, for the gameplay and online segment, it's a turn based battle system with twists. Turn order is determined by overall agility, but you're able to extend turns by uses an enemies weakness (getting an additional to attack for using fire against an enemy who's weak to it). They go into a knocked down/weak state after this, and if you do it to all of the enemies, then you have the option to turn it into a free for all and all of the party members charge in to deal big time damage to all the enemies. The online interaction is limited, but you can see what choices other people made at that point (ex. What people did on the afternoon of 5/11) and in battle, you can SoS for help. When doing so, an notice will appear to everyone in the dungeon so that they can 'send aid'. That will provide a nice boost to your HP and SP before the start of the battle.