First you need to pass subcategories' description from controller to tpl file,
in catalog\controller\product\category.php
find
'name' => $result['name'] . ($this->config->get('config_product_count') ? ' (' . $product_total . ')' : ''),
just after this line add the following line
'description' => strip_tags(html_entity_decode($result['description'], ENT_QUOTES, 'UTF-8')),
Now in your tpl file that is catalog\view\theme\your_theme\template\product\category.tpl
you have to add <?php echo $category['description'];?>
inside the following loop
<?php foreach ($categories as $category) { ?>
<li><a href="<?php echo $category['href']; ?>"><?php echo $category['name']; ?></a></li>
<?php } ?>
P.S. Edit your question to inital one, it was more explanatory than it is now