In this example, the user clicks on the page wanting to find all the blog posts written by the author Joe Lowery. Wordpress will first look for a template file that combines the author's real world name (also known as his "nice name") with the author prefix. If no such template is found, WordPress looks for the author template combined with Mr. Lowery's user ID (23 in this case). If that is not there, WordPress tries to display the generic author.php template. Next up is a theme-specific archive.php template. And finally, WordPress reverts back to the index.php homepage template.
The complete Wordpress template hierarchy can be viewed here (opens in new tab).