get Custom field label (select/dropdown) on front end

You can set the keys of the array to be user-friendly, but more appropriate would be to define the options array in a function, and then use that function in both the backend and frontend (untested):

Array

function product_condition_array() {
    return array(
        'new'            => __( 'New', 'woocommerce' ),
        'like_new'       => __( 'New other (see description) ', 'woocommerce' ),
        'remanufactured' => __( 'Remanufactured', 'woocommerce' ),
        'used'           => __( 'Used', 'woocommerce' ),
    );
}

Backend

woocommerce_wp_select(
    array(
        'id'          => '_condition',
        'label'       => __( 'Condition', 'woocommerce' ),
        'desc_tip'    => true,
        'description' => __( 'Part Condition.', 'woocommerce' ),
        'options'     => product_condition_array(),
    )
);

Frontend

$condition = get_post_meta( … );
$conditions = product_condition_array();
$condition_display = __( 'Unknown', 'woocommerce' );

if ( array_key_exists( $condition, $conditions ) ) {
    $condition_display = $conditions[ $condition ];
}

echo esc_html( $condition_display );

This has the benefit of a single location used by both backend and frontend, so changes are reflected immediately in both locations, simplifying future changes.