TwentyThirteen theme Posts page shows posts instead of page content

The only way you can select a “posts page” is if you have Front page displays set to a static page. If you have Front page displays set to your latest posts, the dropdown selects for Front page and Posts page are disabled.

So, assuming you have Front page displays set to a static page:

  • Front page is the page assigned to display on the site front page. This page’s content is displayed if, per the Template Hierarchy, the page.php template is used to render it. (That may or may not be true if front-page.php or a custom page template is used.)
  • Posts page is the page assigned to display the blog posts index. It is by design that this page displays the main blog posts index, rather than the post_content of the page assigned as the posts page. The Posts page is a special page, that is assigned to this special use.

There are ways for this page’s post_content to be displayed even when assigned as the Posts page, but the Theme would have to account for that explicitly, via the home.php template file, and direct query of get_post( get_option( 'page_for_posts' ) ).