One thing you can do is to use WordPress conditional tags and one example using is_category is explained here.
You can also use function called term_description
and you can read more about it here.
The basic usage would be like this:
<?php
// Show an optional term description.
$term_description = term_description();
if ( ! empty( $term_description ) ) :
printf( '<div class="taxonomy-description">%s</div>', $term_description );
endif;
?>
This outputs description for tags and categories that you can set via WordPress dashboard when editing tags and categories.