Category’s Description field as editor remove tag

How are you outputting the category description? You might need to use something like apply_filters('the_content', category_description( $category_id )); or wpautop(category_description( $category_id )); to have paragraphs in the output.

Edit:
Adding what you had in JSFiddle – note where $term->description is, I wrap it in wpautop. See if that works. If not, try apply_filters('the_content', $term->description) instead:

<?php                   
            $taxonomies=  array('taxonomy'=>'area-type');
            $terms = get_terms($taxonomies,'orderby=id&hide_empty=0');
            $count = count($terms);
            if ($count > 0) {
                    foreach ($terms as $term) {

                        $id = str_replace("#","",$term->slug);
                        $term_desc .= '<div id="nav_menu_desc_' . $id . 
                        '" class="section hidden formateIt">' . 
                        wpautop($term->description) .'</div>';    
                    }                  
                        echo $term_desc ;   
            }   ?>