In the Witcher 3, almost every quest matters. Care and attention is paid to even the smallest, and very few go the way you expect. A prime example of this is in the intro area of White Orchard, where one old lady asks you to fetch a pan for her, and when you find it you discover the man that borrowed it was a spy who wanted the soot off of it to write a letter. It's fundamentally a basic fetch quest, but it's written and designed in such a way to say something about the world.
The highlight of these side quests is invariably the Contracts, where Geralt is commissioned by some town alderman, small noble, or local guardsman to go solve some supernatural problem. Geralt haggles a bit (coin is hard to come by for a wandering monster hunter!), and then goes to investigate. Sometimes it can be routine - find the location of the attack, identify prints and wound marks, and track the beast back to its lair to kill it - but even the most routine contracts take the time to ground their story in the world and establish Geralt as what he is - an experienced Witcher with decades of experience.
Some of these, however, tell self-contained stories as rich and complex as any of the subplots of the main game. The first contract most players will encounter is a great example. Geralt is contracted to clear out a wraith that is haunting a nearby well - but first he has to figure out how to break the curse. In the course of doing so, he discovers a story involving a greedy lord, desperate peasants, and the tragic death of a young woman - who became a Noonwraith, a terrifying spectre who only appears under the bright noonday sun.
Side quests are just as important to establishing a world and a fiction as any of your set piece moments. They generally make up the majority of playtime, and thus are central to establishing the feeling and tone of a game. So the next time you pick up an RPG, think about those side quests you pick up and what they convey about what a game is trying to say. Maybe you'll find more than what you were looking for.