First, H3 tags, or even h4-h6, can also be used outside of the content structure to point out other important sections of a page.
For example, the orange heading below this post that says “Leave a Reply” and all of the headings in the sidebar of this page are H3s. They’re used in this case to indicate to search engines and users that “this is a section of important information” as opposed to being supportive content of a previous H2. While this is somewhat of a misuse of the heading in relation to the content structure, it is still an applicable and acceptable use for the tag.
In practice, we rarely ever use headings past H3s because if your page contains enough content that it needs h4s-h6s, then it probably shouldn’t all be on one page. Instead it should probably be divided into a new category of the site or a main page with sub-pages of supporting & stand alone content.
Just to point out a couple of more things to readers, heading tags don’t have to be large and bold to be a heading. We can make a h1, h2, h3, etc. tag look like anything we want it to…even like this paragraph text that you’re reading now. But, they are very important structural elements of any web document and should be used correctly.
Also, headings should never be used for presentational purposes. Too many people and agencies use heading tags because they need big red text and they think that since headings are big and bold…they’ll just use that! Don’t ever, ever, ever do this. Use a paragraph tag instead and use CSS to make it look how you want.
In short, headings are structural indicators…just like when you’re writing a paper in school. h1 is Main title of the paper, h2 is a section of the paper, h3 is (generally) supporting content or a supporting idea of the h2 and its child content.