Basically shared content is just content without a page context. Usually that is the place to store site logos and content which is identical on all pages across your website. You can also choose your globally used theme here. Conceptually, shared content can be seen as the default content for all pages.
When setting a value for a variable in the Shared Data & Settings section, that value becomes a default for any page using a template including that variable. Page content has always a higher priority when rendering templates. That means as soon you set a value of a variable in a page context, the shared value is ignored. Typically shared data is used to provide a standard text for footers or a default glob pattern for file selections.