Radiant storytelling appears to be a feature that Bethesda used in the making of Skyrim that acts as a narrator for your character in the world. It records your actions and changes things in the world according to what you have done - for example, if you murder someone, their family will find out, as well as the community. It also adjusts game difficulty depending on your skills and changes different things in quests such as different reactions or outcomes depending on how you play, like deciding to not enchant armor you're supposed to as a favor for someone out of your own money; he would then pay you back. If you sell the armor instead, Radiant Story would adjust the quest to your preference.
You won't find townspeople loitering aimlessly in town squares anymore. Each citizen performs tasks that make sense in their environment. To impart the towns and cities with a greater sense of life, Bethesda has populated them with mills, farms, and mines that give the NPCs believable tasks to occupy their day. The improved Radiant AI technology is also more aware of how a citizen should react to your actions. As you perform tasks for them or terrorize them by ransacking their home, the NPCs develop feelings about you. If you're good friends with a particular NPC and barge into his house during the middle of the night, he may offer you lodging rather than demand you leave the premises. If you swing your weapon near an NPC, knock items off their dinner table, or try to steal something of value, they'll react with an appropriate level of hostility given their prior relationship to you. Another good example of this is that if the player clears the Kolskeggr mine, near Markarth, of all hostile AI - as a miscellaneous quest accepted from Pavo Attius - and return to him, an Orc by the name of Gat gro-Shargakh will make a comment saying that he has informed all Orc stongholds in Skyrim of your good deed and consequently they will not be hostile towards the Dragonborn.
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. Radiant Story is also smart enough to know which caves and dungeons you've already visited and thus conditionalize where, for instance, a kidnapped person is being held to direct you toward a specific place you haven't been to before, populated with a specific level of enemy. Skyrim also tracks your friendships and grudges to generate missions. Do a small favor for a farmer and it may eventually lead to a larger quest. Some NPCs will even agree to be your companion to help you out in specific situations. This proves very useful when fighting enemies.