To understand
Shin Megami Tensei: Persona 3, you first need at least a general idea of the
Shin Megami Tensei series background. Complete and total ignorance of the series won't completely ruin the game, but having a framework should shave off some of the "weirdness" that is a large part of the series. Though there have been exceptions, most of the series takes place in modern settings where humans and demons co-exist. How much humans know of the existence of demons varies with each game. In
Persona 3, humans are more or less ignorant of demons. In fact, when the demons are out, most humans are asleep in their coffins... oh wait; yeah there's that whole "weird" thing I was talking about.
Persona 3 revolves around a group of Japanese high school students who have the power to summon Personas, or friendly demons, to combat Shadows, which are the bad sort of demon. Shadows only come out during "The Dark Hour," which is the hidden period of time between midnight and 12:01 am. People who can summon Personas are aware of this time period, while everyone else turns into a coffin. The unfortunate souls who don't enter coffins and can't summon a Persona usually become the Shadow's victims.
Playing as a brand new student at Gekkoukan High School, you are one of the lucky few who can summon a Persona. A few of your classmates are quick to sniff out your power and recruit you into their club to help combat the Shadows. Every night during the Dark Hour, a tower called Tartarus appears near the school. Combat is only half the experience; Persona 3 is equal parts "traditional" RPG and Social simulation.
Combat is confined to the multi-floored Tartarus. A majority of the floors are randomly placed, though there are a few "rest stops" containing teleporters that allow you to quickly travel between that floor and the ground floor. This cuts down on the boring trudges through already cleared floors and also guarantees a save point before boss battles since teleporters and bosses tend to appear within close proximity of each other.
The 24 hours spent outside the Dark Hour are spent planing out your character's social life. You can decide to be a jock, the smart kid or Mr. Popular. Regardless of your social ambitions, every social connection you make at school directly influences your Persona. Taking part in sports will increase your relationship to a Personas that share a relationship to that trait and give it bonuses, making it stronger when you summon it. Though it may seem like a throwaway time waster, bonuses earned though social means can allow your Persona's stats to increase beyond their normal capabilities, which is sure to help while fighting through Tartarus.
The play between Social and Combat is handled well. The two integrate so well that if you become stuck in one element, you can always focus on another and gain some sort of movement. If your social standing is taking too much of a hit, you can avoid Tartarus and focus solely on that - giving you that added extra time. Doing so will also help to increase your Persona's power, making the trek through Tartarus easier.