$category = get_category($latest_issue); // it is category object
echo $category->title;
echo $category->description;
in codex: http://codex.wordpress.org/Function_Reference/get_category
But i think you should get category not by last created ID, but by slug:
http://codex.wordpress.org/Function_Reference/get_category_by_slug
So you should change:
<?php $issue = get_terms('category', 'orderby=ID&order=DESC&number=1&child_of=3'); $latest_issue = $issue[0]->term_taxonomy_id; ?>
<?php query_posts(array( 'category__in' => $latest_issue )); ?>
to
<?php $issue_category = get_category_by_slug('issue'); ?>
<?php query_posts(array( 'category__in' => $issue_category->term_id )); ?>
and to print your category title and description:
echo $issue_category->title;
echo $issue_category->description;