hook_action_info.php

<?php

/**
 * Implement hook_action_info
 * @return array array with the new actions
 */
function module_name_action_info() {
  return [
    'name_of_callback' => [
      'label' => t('Notify after comment'),
      'type' => 'comment',
      'configurable' => FALSE,
      'triggers' => array('comment_insert'),
    ],
  ];
}

/**
 * @param   object $comment
 * @param array $context
 *   Array with components:
 *   - 'keywords': Keywords to look for. If the comment contains at least one
 *     of the keywords, it is unpublished.
 */

function name_of_callback($comment) {
  //Here be dragons
}

?>