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_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_category_description_single_event' );

function ee_display_category_description_single_event( $post ) {
    $taxonomy = 'espresso_event_categories';
    $terms = get_the_terms( (int) $post->ID, $taxonomy );
    if( !empty( $terms ) ) {
        foreach( (array) $terms as $order => $term ) {
            if( !empty( $term->description ) ) {
                $description = $term->description;
                echo '<p>' . $description . '</p>';
            }
        }
    }
}