I know very little about Dragonronpa outside of a few of my friends REALLY liking the series, I saw the first arc of the anime adaption but stopped after the first court case was done because I decided I wanted to play the game, and a few other things.
From my limited knowledge, what I know about it is that a bunch of kids with really weird hair and quirky personalities (many of them hardly anime cliche personalities, they're like, very odd characters in general) get trapped in a school. There is a weird bear with a twisted personality who tells them that they can only graduate (IE escape from the school, but also those who escape are also rewarded with a certificate that apparently will get them about any job or position they desire) if they can kill one of the other students and get away with it.
When a student has been murdered, there's a time limit to discover evidence and investigate until a trial is held. At the trial, the student body must work together and make a unified decision on which student was the killer. If they guess correctly, the culprit will be executed and not be allowed to graduate. If they guess incorrectly, all of them will be executed and the killer will be let free and graduate.
I might be off on a few things since I'm saying from memory what I know from the first few episodes of the anime and what friends said, but that's the gist of it.
I also know the second game has a parody mini-game (part of a series of arcade-themed mini-games, I guess since this is the 2nd one of a series) based off of a really obscure horror game series known as Twilight Syndrome, which was the first game series Suda51 ever worked on (second game he ever worked on in general). The reason for the reference was because some of the people who make these games worked on the Twilight Syndrome series previously (Japanese-exclusive horror games that started on the PSX that Suda51 directed again).