Depending on whether you intend to use this template to display other categories elsewhere, you may need a copy of the Portfolio Template file, named for this category.
To select a single category for display, from post type ‘portfolioitems’, modify the following line:
$wp_query = new WP_Query(array('post_type' => 'portfolioitems','posts_per_page' => 50,'paged'=> $paged));
To:
$wp_query = new WP_Query(array('post_type' => 'portfolioitems', 'cat=4', 'posts_per_page' => 50,'paged'=> $paged));
This assumes the ID for your desired category is 4. Simply adding an extra key/value to the WP_Query array will include that filter and exclude any post that does not match the extra criteria.
You can filter category by name, ID, etc. The various methods available are detailed here.
WP Codex ref for category parameters.
** EDIT to taxonomy query **
Based on this additional information, you appear to need a taxonomy filter specific to the custom post type ‘portfolioitems’.
$wp_query = new WP_Query(array('post_type' => 'portfolioitems', 'section' => 'sectionname', 'posts_per_page' => 50,'paged'=> $paged));
Replace ‘sectionname’ with the name of your desired section. Full details on taxonomy parameters