If you have a look at how [dj-widget] shortcode is handled you will get an idea of how to implement plugin authors’ idea of showing post description.
if($show_desc) {
$desc_string = station_shorten_string(strip_tags($show->post_content), 20);
$output .= '<span class="on-air-show-desc">'.$desc_string.'</span>';
}
insert this between $output .= '<li>...' and $output .= '</li>';
Please NOTE: There might be a better way to show actual post excerpt instead trying to generate one based on post content. More here.