For The Events Calendar. This will show the event category description below the title. This example only shows in list view. Place in functions.php

show-category-description.php

<?php

add_action( 'tribe_events_after_the_title', 'my_category_description' );

function my_category_description() {
	global $wp_query;
	if( !isset( $wp_query->query_vars['post_type'] ) or !isset( $wp_query->query_vars['eventDisplay'] ) or !isset( $wp_query->queried_object ) ) return;
	if( $wp_query->query_vars['post_type'] === 'tribe_events' or $wp_query->query_vars['post_type'][0] === 'tribe_events' and $wp_query->query_vars['eventDisplay'] === 'upcoming' )
		echo '<div style="text-align:center;">' . $wp_query->queried_object->description . '</div>';
}

Updated to check of $wp_query->queried_object

Now works for both single and multisite