WordPress – add help text under category list(right side) in post edit page

There is not available action and filter hook to modify of taxonomy meta boxes html like admin_post_thumbnail_html. so here is a trick to add descrition below category.you have to create new metabox for help then move to category div.

# Add new meta box for help description
add_action( 'add_meta_boxes', 'add_help_desc_meta_box', 0 );
function add_help_desc_meta_box() {
    global $wp_meta_boxes;
    add_meta_box('description-help-desc-meta-box',__('Categories Help Description'),'description_meta_box_callback','post','side','low');

# here you can add your description
function description_meta_box_callback()
    echo "<p>Here is your description</p>";

#you can append your help desc meta box to category
function cat_help_description_meta_box_move() {
        (function($) {
add_action( 'admin_head', 'cat_help_description_meta_box_move' );

let me know if this helps you!