There are two subject in this and I'll start with the second, because it's shorter.
Why you mark sections of stories apart.
Traditionally you cut stories into section because there is a change of subject, or a change of act, or a change of scene, or a change of location, or a change of time, or s change of point of view. When and how you cut to or from any of these changes is another subject, and will vary between authors and style manuals used.
An extremely important time to change is when you change the center of focus or change the point of view. This most important if writing in the first person. When you change from Fred's POV to Jack's POV you need a very clearly marked change point so the reader doesn't get confused. A change of POV is like a change of speaker in dialogue, it must be well marked and clearly identified, but with a change of POV it must be marked at each change.
I don't do this much, but did do it in Rough Diamond where I used a new chapter or sub-chapter for each new person when I changed the POV from the main character to another person. I made sure the title I assigned let the reader know who's point of view it was when it wasn't that of the main character, because the story is in the first person.
Types of change markers used
The most common types are chapter headings, sub-chapter headings, section headings, horizontal rules (full or partial), or other substitute characters for a horizontal rule - like a line of stars or dashes or an image. With some major works they also do it by having it as another book - got to be huge and well written to make this one work for you.
Part of the problem today is more and more people are writing for on-line display, and thus the more traditional choices of chapter, sub-chapter, and section heading are being ignored due to them not working out how to translate them into an on-line display. Thus horizontal rules and their variants are becoming more frequently used.
With a small extra effort you can use on-line equivalents of chapter, sub-chapter, and section headings. It simply requires setting up a suitable style sheet for you work in whatever you use to write your story. If you use a word processor it's easy to do by setting heading and paragraph styles.
NB: If you wish to create an e-pub or similar e-book from your work you need to be wary of what styles you use. For chapter, sub-chapter headings, and section headings. Most word processor programs will have a style for Heading - Heading 1 - Heading 2 - Heading 3 - etc they go down to Heading 10 in most software. If you use H1, H2, and H3 the software will recognise and swap them over into HTML or the XHTML used for most e-books, but it won't always handle the first level Heading (note no number) the correct way.
Also, some e-pub software eliminates some format code from the text, so you need more than just the H1 or H2 designator to differentiate them. This is also true for the HTML display through some sites.
It's been my experience that using the full range of the change markers provides a greater flexibility in the delivery and presentation of the story with the maximum amount of clarity for the reader of the story.
I write all my stories in a word processor (Libre Office) with a pre-set format of my own that uses chapter headings (H1 in bold red text), sub-chapter headings (H2 in bold blue italic text), section headings (H3 in bold) with all the headings centered in the line. I also use a half page ruled line to break up some scenes and other divisions I feel I need within a chapter / sub-chapter / section for something like notes etc. - Not all chapters need or have a sub-chapter and not everything requires a section, either. They are used as the needs of the story dictates. Also, in most software the different headings display in different sizes with the lower number being a bigger font.
The centered title helps the reader to know there is a change, and also gives them some clue as to what the change is about or for, especially if the title is well chosen.
Each chapter and sub-chapter starts on a new page within my book format. This carries across to the e-pubs I make.
edit to add: In a web page display of the html it displays as one long page unless a specific effort is made to make them different web pages - which i don't do. Thus the headings show as varied sized coloured titles in the middle of the line in the story text.
To make a html file from the book format I simply 'Save as' .html and the software adds the html code. However, I do need to use a suitable edito (not the word processing program) to strip out some excess code because word processors format each paragraph where html tends to format only changes. The result is way too much code in the file as first saved in html. Using a 'Find and replace all' makes removing it easy when you replace it with nothing.
One other thing I do to get my story file ready for SoL is to change the H3 to H5, the H2 to H4, and the H1 to H3 - in that order, because SoL already uses H1 and H2 for other things. Change the H3 to H5 first or you can get the H1 ending up as H5 as well. You also need to include the command to center and color some of the headings. There is a little more I do with some of the other things, but that's for other presentation aspects.