It serves to create a world which is an immersive simulation, and not a simple narrative. It records player actions and alters parameters within the world in response to player actions. For example, if the Dragonborn murders an NPC, the family and community may find out, which may trigger a related quest or initialize an attack by assassins. Dropping an item in specific locations may initiate an NPC conversation, requesting to either return or keep the dropped item. It also adjusts game difficulty depending on player skills and can modify reactions, encounters, and outcomes based on player style.
Townspeople no longer loiter aimlessly in town squares. Each citizen performs tasks that make sense in their environment. To impart the towns and cities with a greater sense of life, they are populated with mills, farms, and mines which give the NPCs believable tasks to occupy their day. The improved Radiant AI technology alters NPC responses based on in-game action. As the player character helps by performing tasks, or harms by ransacking an NPC's home, the NPC develops "feelings" about the player. For example, if the player character is in good standing with an NPC and barges into their house during the night, the NPC may offer them lodging rather than demanding the player leave the premises. If a weapon is swung near an NPC, items are displaced from proper positions, or an attempt to steal something of value is discovered, they'll react with an appropriate level of hostility given their prior relationship to the offender.
A good example is as follows: if the player character clears Kolskeggr Mine as a miscellaneous quest accepted from Pavo Attius, an Orc by the name of Gat gro-Shargakh will speak to the player indicating he has informed all Orc stongholds in Skyrim of the good deed. Consequently, they will not be hostile towards the player when encountered.
While main quests are fully structured, 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 with a string of unrelated and mundane tasks, it tailors missions based on who the character is, where they are at, what they've done in the past, and what they're currently doing. Radiant Story is also smart enough to know which caves and dungeons the Dragonborn has already visited. For instance, a kidnapped person is being held to direct the player towards a specific place they haven't been to before, populated with appropriately leveled enemies.
Radiant storytelling allows the game world to develop organically beyond the stories set by the developers, and creates a novel and sometimes serendipitous experience for the player.