What «heading structure» means
A heading is not large text. It is a semantic element that states two things at once: a section starts here, and this section hangs off that other one. The rank is set by the number of the element, from h1 to h6, and that number is the only part machines read.
That is where the most common confusion comes from. Visual size and semantic rank are independent: a stylesheet can make an h4 look huge and an h2 look modest. Choosing the element by how it looks on screen destroys the structure without anything warning you.
The concept needs boundaries against three neighbours. The title element is the document title and lives in the head, outside the content. The table of contents is navigation built from the headings, not a replacement for them. And the subtitle, the claim or the standfirst are not headings: the standard provides for grouping them with the title inside an hgroup, as a paragraph.
Structure in the strict sense is the list of every heading in the document, in the order they appear, with their rank. That list is exactly what someone navigating with a screen reader moves through.