When is a module shown as 'Unsupported' in the list of available updates?
In Drupal 8, that string is output from UpdateManagerUpdate::buildForm(), which contains the following code.

  case UPDATE_NOT_SUPPORTED:
    $type = 'unsupported';
    $entry['title'] .= ' ' . $this-&gt;t('(Unsupported)');
    $entry['#weight'] = -1;
    break;


The UpdateManagerInterface::NOT_SUPPORTED constant simply means the current release is no longer supported by the project maintainer. The maintainer doesn't intend to further develop the module code, not even to fix security issues. If you look at the project page, you will notice the following note, given under the Project information section.


  Unsupported
  Not supported (i.e. abandoned), and no longer being developed. Learn more about dealing with unsupported (abandoned) projects


As such, the update page is suggesting to find another module with the same, or similar, features because, in case of security issues, chances are nobody is going to fix them, and the module would need to be uninstalled, to avoid site issues.

In Drupal 7, a similar string is output from theme_update_status_label(), which contains the following code.

case UPDATE_NOT_SUPPORTED:
  return '&lt;span class="not-supported"&gt;' . t('Not supported!') . '&lt;/span&gt;';


The UPDATE_NOT_SUPPORTED constant has the same meaning saw for Drupal 8, and it was introduced in Drupal 6.