You mean this menu? (screenshot)
That menu is mainly there to allow modules to add menu items to. So if you're thinking to do it from a module, then the code is:
$_tmp = array(
'group' => 'user',
'label' => 'Profiles You Follow'
'url' => 'following'
);
jrCore_register_module_feature('jrCore', 'skin_menu_item', 'jrFollower', 'following', $_tmp);
^^ code taken from the jrFollowers module's _init() function in include.php.
You'd do the same from your module.
Purpose of it is to allow modules to add themselves to the skin without the need for the owner of the skin to do any customization to get the module to work.
--
If you're wanting to add a static item onto the end or the beginning of that, you can do it without building a module by customizing the menu.tpl file in your skin.
/skins/(YOUR SKIN)/menu.tpl
It probably looks like this
{foreach $_items as $entry}
{assign var="oc" value=""}
{if isset($entry.menu_onclick) && strlen($entry.menu_onclick) > 2}
{assign var="oc" value=" onclick=\"`$entry.menu_onclick`\" "}
{/if}
{if isset($entry.menu_function_result) && strlen($entry.menu_function_result) > 0}
{if is_numeric($entry.menu_function_result)}
<li><a href="{$entry.menu_url}" {$oc}>{$entry.menu_label} [{$entry.menu_function_result}]</a></li>
{else}
<li><a href="{$entry.menu_url}" {$oc}>{$entry.menu_label} <img src="{$entry.menu_function_result}" alt="{$entry.menu_label}"></a></li>
{/if}
{else}
<li><a href="{$entry.menu_url}" {$oc}>{$entry.menu_label}</a></li>
{/if}
{/foreach}
so if you add another LI at the end it will show up in the menu
<li><a href="https://jamroom.net">A link to Jamroom.net</a></li>