This post deals with the storytelling inherent in the craft of writing itself, not the craft of fictional narratives, character arcs, worldbuilding, or anything to that effect.
While we tend to think of the "overarching narrative" as our story when writing -- the whose and whats and whens and wheres across an entire novel or whathaveyou -- there are also stories present in the experience of reading itself. Every sentence that we write is an inherent story. After all, why should someone listen to us, amidst everything else they could be doing with their life?
Besides whatever overarching goals a listener might have, such as to learn a certain topic or find out what happened to the damsel in distress, they also have goals unique to the reading experience, and the tension is affected by how we choose to structure our sentences, paragraphs, scenes, chapters, and so forth.
These may vary by language, so just be aware that I'm speaking from the perspective of an English writer.
Sentences as Story
When a listener approaches a sentence, their first goal is usually, what is this sentence about? Meaning, who or what are the actors -- the subjects who are doing something and objects who are having something done to them. The next goal is usually, what is happening? Meaning, what are they doing, or what is being done to them -- the predicate of the sentence. The goal then is typically, in what manner is it happening or the specifics of when and how exactly -- our adjectives, adverbs, and such. Even though these are technically classified as parts of the subject or predicate, they are not necessarily part of the listener's top-level goals.
(There is also, of course, the goal to merely complete the sentence and continue progressing through the prose! That final punctuation is the ultimate resolution of the sentence that provides the most relief.)
In English, we frequently split our subject and object between the beginning and end of the sentence, as we have the secondary subject the action is being done to after the action. "He hit her," for example. In some other languages, such as Japanese, it's common to define all of the actors and their roles before the action. "He (subject) she (object) hit," for example. Small phrases called "particles" are used after each noun to define its role in the sentence in Japanese, so it can techincally be ordered in any way, but the common convention is to set the stage first.
In this way, each language's simplest sentences already have some inherent storytelling to them. In English, you're waiting in anticipation to find out 1) what action is being done, then 2) who the action is being done to. In Japanese, you're waiting in anticipation to find out 1) what role each actor is playing, then 2) what action is being performed. Of course, this anticipation is very short-lived in a short sentence.
We can then vary up how we choose to structure our sentences to manipulate the experience of that story. In English, we can split complex sentences using commas, allowing us to rearrange each part of the sentence. "To rearrange each part of the sentence, in English, we can split complex sentences with commas." Some subtle changes may be required depending on the phrasing.
As in any form of storytelling, the more obstacles there are between the listener and their current goal -- the excess words, the convoluted vocabularies, the complex grammatical choices and interjections -- the more tension you induce in the listener. Carrying a sentence on for a long period of time can create intense stress. When it then ends in a wonderful resolution to an overarching goal, or some other rewarding twist, it pays off by providing an emotionally satisfying rollercoaster.
So it's not just the ordering of the words that alters the experience but also the types of words and how many you use.
Things like pacing and rhythm also play a big role. If it feels like every sentence is the same, the brain starts to feel like it's chasing the same goal -- solving the same problem -- over and over again. It loses interest. Remember that we are pattern recognition machines. You are constantly fighting that human instinct, trying to tweak your structures here and there, while never following the same patterns of sentence types in a sequence.
The same then applies to your paragraph structures. Their lengths, their arrangements. If they're too similar, the brain starts assuming they're the same and skips over to what seems new and interesting. So you are carefully varying things to keep a listener's interest.
This type of psuedo-randomness / contrived informality is extremely difficult to achieve, and it's one of the things you'll be fighting with the most when editing a work of prose.