Add category information beneath post?

The simplest solution would be a simple filter on the_content:

function my_affiliates_descr($content) {
 if (is_single() && has_category('affiliate')) {
  $content .= 'This is an affiliate post';
 }
 return $content;
}
add_filter('the_content','my_affiliates_descr');

You could combine that with category_description() as suggested in a comment to the question to get:

function my_affiliates_descr($content) {
 if (is_single() && has_category('affiliate')) {
  $content .= category_description( get_category_by_slug('affiliate')->term_id );;
 }
 return $content;
}
add_filter('the_content','my_affiliates_descr');