Output the term’s description instead of its name

<?php

// Change "categories" to the name of your facet

add_filter( 'facetwp_facet_display_value', function( $label, $params ) {
    if ( 'categories' == $params['facet']['name'] ) {
        $term = get_term_by( 'id', $params['row']['term_id'] );
        if ( ! empty( $term ) && ! empty( $term->description ) ) {
            $label = esc_html( $term->description );
        }
    }
    return $label;
}, 10, 2 );