This will display the categories.
<?php
$args = array('taxonomy' => 'product_cat');
$terms = get_terms('product_cat', $args);
$count = count($terms);
if ($count > 0) {
foreach ($terms as $term) {
echo '<p>' . $term->description . '</p>';
}
}
?>
Where you put it depends on your theme. In your theme or child theme you need to create these folders woocommerce > single-product > meta.php
.
You will most likely need to edit the above code for your needs but it should give you an idea.