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<?php
    $taxonomyName = "cpt_rankings_cat"; // Set your custom taxonomy here.

    // Alternate method for retrieving a term ID. Source: http://codex.wordpress.org/Function_Reference/wp_get_post_terms#Examples
    $term_list = wp_get_post_terms($post->ID, $taxonomyName, array("fields" => "ids"));

    // Source: http://codex.wordpress.org/Function_Reference/get_term_children#A_Basic_Example

    $term_parent_ID = $term_list[0]; // Pulls the parent term ID from the call above.

    // Use the following get_terms in order to have them sort by name. Source: http://wordpress.stackexchange.com/a/17148
    $term_children = get_terms( $taxonomyName, array(
        'child_of' => $term_parent_ID,
        'orderby'  => 'term_group',
        'order'    => 'ASC',
        ) );


    foreach ($term_children as $term_child) {

        $term_args = array(
            'tax_query'         => array(
                array(
                    'taxonomy'     => $taxonomyName,
                    'field'        => 'slug',
                    'terms'        => $term_child->slug, // Calling the single child term here.
                ),
            ),
            'post_status'       => 'publish',
            'posts_per_page'    => -1,
            'orderby'           => 'date',
            'order'             => 'DESC',
        ); // END $term_args

        $term_query = null;
        $term_query = new WP_Query($term_args);

        if( $term_query->have_posts() ) {
            echo '<h3>' . $term_child->name . '</h3>'; // Placed the term name here so it won't display if it doesn't have any posts.
            echo '<p>' . $term_child->description . '</p>'; // If your term has a description, it will show.

            echo '<ul>';
            while ($term_query->have_posts()) : $term_query->the_post(); ?>
                <li><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a>
                </li>
            <?php
            endwhile; // END while have_posts
            echo '</ul>';

        } // END if have_posts
        wp_reset_postdata();
    } // END foreach
?>