What is the nature of Skyrim's infinitely generated quests?

According to this Gameinformer article from January, which is in turn based on an interview with Bethsoft creative director Todd Howard, the quests are "parametrized templates". The article gives the example of an assassination quest template, with its parameters populated programmatically according to your character's behaviour and past NPC contacts:

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.”

The parameters are filled in by a system that watches what you're doing, where, and with whom. Based on your actions, it builds a catalogue of things that can be slotted into quest templates as needed:

The story manager is always watching you, which can leads to strange random encounters as well. If you drop a sword in the middle of town, someone may pick it up and return it to you, or two guys may get into a fight over who gets to take it. If you're really good at a particular skill, like one-handed weapons or destruction spells, a stranger who knows of your reputation may ask for training, challenge you to a duel, or beg you for a favor that will require you to show off your skill.

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.

So there are a fixed number of quest templates in, which are used to generate the "infinite quests". With a large enough number of such templates of sufficient variety, and a smart enough system to figure out interesting relations between your character and NPCs, dungeons, and items, the randomly-generated quests would remain interesting for quite a while.

Well, infinite, yes. However, some quests may repeat. Such as, (just an example from my thousands of in game years playing) "Steal Ysolda's ring." Which I've got seventeen times.