Author Kurt Vonnegut talked about what he called the shapes of stories. One of the basic plots he described, Man in Hole, starts at a high point with the protagonist doing well, then they are brought low by falling into some trouble, and finally they get to another high point after resolving their troubles. Novels and TV shows that capture popular attention often follow such structures. Many shapes are studied and reproduced meticulously in today's blockbusters, like Joseph Campbells Hero's Journey, where the hero embarks on an adventure, encounters adversity, and then returns home changed.
Many game masters will write stories ahead of time, and guide their adventuring party through a predetermined set of events. In this case, a campaign may have a well defined shape, where clear recognizable plot points occur to give a story different progressions of highs and lows.
There is a way that stories develop in games if the GM refrains from writing a story before hand that I think of as an aggregate story arc. In a game that values player agency, the highs and lows come much more randomly and unpredictably. So you have little chapters and vignettes that tie together probably leading towards one or a handful of overarching quests or themes. They are more or less a series of collisions between players and the game world. Ultimately there is a story shape or arc, but it is an aggregation of many different things that happen over the course of months and years of playing to find out what happens next.
I had a moment in a recent game I run, where following a players curiosity and improvisation based on random tables felt very much like one little chunk of a larger aggregate campaign arc. The group was traveling by boat through a jungle when their boats were damaged by rocks. They spent the evening and night on a river bank doing repairs, and in the meantime one of the characters (the thief of course) decides to wander into the jungle looking for anything valuable. After a few rolls of the dice and some random generators, we found out that they do in fact find something. It was a giant ameoba with a glowing flower in it, strangely undigested inside the amoeba's body beside bits of decomposing debris. The players use a bag of salt that they happen to be carrying to easily overcome the amoeba and recover the flower, which they will be able to use to create a regeneration potion. They discussed some plans, which included trying to cultivate and grow more of this flower. The regeneration flower could be a footnote, or it could be the start of a new agricultural dynasty.
This was one short chapter among many in our campaign, made up on the spot, but memorable and potentially game changing. It seems to me that these little chapters aggregate, being created through randomness and letting things happen spontaneously and organically. Events layer one after another to create a richly varied, moving story line that is much more satisfying than any prewritten plot arc.