This WordPress snippet will allow you to show the image caption for the featured image in your WordPress posts without using a plugin.

Add this code to your theme files (ie. single.php) where you are displaying the image.

<?php if (get_post( get_post_thumbnail_id())->post_content);  // check if image has caption added // ?>
   <div class="featured_image_caption">
      <?php echo wp_kses_post(get_post( get_post_thumbnail_id() )->post_content ); // outputs image caption // ?>
<?php endif; ?>

*you can replace post_excerpt with post_content to get the image description etc.