Headings, lists, tables and emphasis all help the user to read and understand your content, by distinguishing one block of content from another and thereby establishing a structural relationship between them.
In all of these cases, the relationship is communicated visually. Headings might be displayed in a larger font and separated from the preceding paragraph text, lists may be indented with item lines identified by a symbol, tables are useful for laying out data in columns and rows, and emphasised text is typically bold or italicised.
The visual nature of the way this kind of formatting establishes the relationships between sets of information on a webpage means they may be inaccessible and the information thus incomplete.
If a person is blind or vision impaired they will not see the formatting and not receive information about relationships between pieces of content that a sighted person will.
The way to address this is to make sure the information about content relationships is presented in a way that can be perceived by assistive technology and effectively conveyed to the user. This can be done using HTML.
The intent of Success Criterion 1.3.1 Info and relationships is to ensure that any information or relationship shown visually using formatting is also made available to assistive technology users.
Let's look at two examples.
The text for the line intended to be a heading has been manually styled: the font size has been increased to 16pt and the text has been made bold.
A heading style has been applied. When that style is applied, the heading is 16pt bold font and the heading is identified using a heading tag.
Visually, the output of both examples will be identical in all web browsers. However, for assistive technology such as a screen reader, these pieces of text are quite different. A screen reader will describe Example 1 as simply a piece of text that is in 16pt bold font.
In Example 2, the heading tag allows the screen reader to tell the user that this piece of text is a heading. It will typically not relay the formatting to the user, just the fact that this is a heading at level one. What is conveyed to the user is the relationship between the information in the heading and the content that follows it.
The semantic meaning that comes with using the right HTML tags in the right situation is extremely important for assistive technology users. For a content writer, this means not only using heading tags, but using them appropriately to preserve the hierarchy of meaning conveyed to the sighted user by formatting.