Display the description for the category/categories that are assigned to a single event. Requires Event Espresso 4. You can add this code to a <a href="http://eventespresso.com/wiki/create-site-specific-plugin-wordpress-site/">functions plugin</a> or into your WordPress theme's functions.php file.

display_event_tags_and_categories.php

<?php
//* Please do NOT include the opening php tag, except of course if you're starting with a blank file

add_action( 'AHEE_event_details_before_the_content', 'ee_display_tags_and_categories_single_event' );

function ee_display_tags_and_categories_single_event( $post ) {
    $taxonomy = 'espresso_event_categories';
    $terms = get_the_terms( (int) $post->ID, $taxonomy );
    $tags = get_the_tags( (int) $post->ID );

    // Output event categories
    if( !empty( $terms ) ) {
        foreach( (array) $terms as $order => $term ) {
            if( !empty( $term->description ) ) {
                echo '<h4>' . $term->name . '</h4>';
                echo '<p>' . $term->description . '</p>';
            }
        }
    }

    // Output event tags
    if( !empty( $tags ) ) {
        echo '<ul>';
        foreach( (array) $tags as $tag ) {
            echo '<li>' . $tag->name . '</li>';
        }
        echo '</ul>';
    }
}