If you want your category links to provide the description in the link alt attribute (which I assume is what you're after), you'll have to edit the source for this. If you're up for *that*, the file is
wp-includes/template-functions-category.php
Look for the function list_cats, towards the end of that file. Then search out this section:
if ($use_desc_for_title == 0 || empty($category->category_description)) {
$link .= 'title="'. sprintf(__("View all posts filed under %s"), wp_specialchars($category->cat_name)) . '"';
} else {
$link .= 'title="' . wp_specialchars(apply_filters('category_description',$category->category_description)) . '"';
}
Change it to this:
if ($use_desc_for_title == 0 || empty($category->category_description)) {
$link .= 'title="'. sprintf(__("View all posts filed under %s"), wp_specialchars($category->cat_name)) . '"';
} else {
$link .= 'title="' . wp_specialchars(apply_filters('category_description',$category->category_description)) . '"';
$link .= ' alt="' . wp_specialchars(apply_filters('category_description',$category->category_description)) . '"';
}