Show category meta in loop on homepage

$category = get_category($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;