A function that displays the caption for a featured image.

the_post_thumbnail_caption.php

<?php
function the_post_thumbnail_caption() {
  global $post;

  $thumbnail_id    = get_post_thumbnail_id($post->ID);
  $thumbnail_image = get_posts(array('p' => $thumbnail_id, 'post_type' => 'attachment'));

  if ($thumbnail_image && isset($thumbnail_image[0])) {
    echo '<div class="caption">'.$thumbnail_image[0]->post_excerpt.'</div>';
  }
}
?>