Solution - 1

I was going to publish a similar tutorial in my site in a few days. Here's the modified code of it, to insert description inside em

add_filter('walker_nav_menu_start_el', 'description_in_nav_el', 10, 4);
function description_in_nav_el($item_output, $item, $depth, $args)
{	
	return preg_replace('/(<a rel="nofollow" .*?>)/', '$1' . "<em>{$item->post_content}</em>", $item_output);
}

<a rel="nofollow" href="#"><em>The Description</em>A Category</a>

Solution - 2

can i help you? you want to show the category description? or you want to show the description of the nav_menu witch is relates to the category?

Solution - 3

Try this

<?php echo category_description(5); ?>