What exactly does the radiant story do?
I sorta get it, but I don't really get the random quest thing or whatever.
I think it's similar, but hopefully more advanced, to Red Dead Redemptions random encounters. They apparently have it so that the random quests are relevant to the current events of the game, as well as past events.
Before they started planning missions for Skyrim, Howard and his team reflected on what they liked about their older projects. They kept returning to the randomized encounters in Fallout 3 and Daggerfall. To build off the success of those models and improve the experience so the random encounters feel less forced or arbitrary, Bethesda undertook the ambitious task of constructing a new story management system dubbed Radiant Story. Many quests are still completely governed by Bethesda, but the Radiant Story system helps randomize and relate the side quests to players to make the experience as dynamic and reactive as possible. Rather than inundate you with a string of unrelated and mundane tasks, it tailors missions based on who your character is, where you're at, what you've done in the past, and what you're currently doing.
“Traditionally in an assassination quest, we would pick someone of interest and have you assassinate them,” Howard says. “Now there is a template for an assassination mission and the game can conditionalize all the roles – where it happens, under what conditions does it take place, who wants someone assassinated, and who they want assassinated. All this can be generated based on where the character is, who he's met. They can conditionalize that someone who you've done a quest for before wants someone assassinated, and the target could be someone with whom you've spent a lot of time before.”
EDIT: I remember reading somewhere that things such as family of killed NPCs may take over businesses. So if the original owner died from some event in the game, such as the above mentioned assassination, a family member may take over and continue selling goods.