Sections, as opposed to the Tags and Byline taxonomies are primarily related to site structure and navigation. It is perhaps best thought of as placing an article inside of a navigation menu.
The sections metabox looks like this:
An article can have any number of Sections or Sub-Sections. These are indicated by the check boxes in the metabox. An article will appear on all of the section start pages for which the checkbox is checked.
An article may have 0 or 1 “Primary Section”. This is the section that displays on the articles teaser card.