If you are using the Drupal Metatag module it might happen, that the meta tags are not shown on the front page despite the fact that you defined them with "Global: front page". And this happens while they are shown on all the other pages.
One very typical reason is, that your theme has a specific configuration for the front page, that doesn't print the content section ($page['content']). This occurs for example with themes from More than themes if the "Drupal frontpage content" option is disabled. Another reason might be that the theme has a specific php file for the front page (Example: page--front.tpl.php) that doesn't print the content section.
To fix this you just add the following lines to the page.tpl.php
or these line to the page--front.tpl.php