The site and page descriptions, also called Meta description, will appear in the search results under the page url. The description has no effect on the page ranking but can draw attention to your site in the search results. Make sure to write a clear, unique & compelling description to encourage the visitor to click on your site.
You can edit the site description under Settings > General > Website > Site meta description.
You can edit the page description in the Edit this page > Settings > Meta description.