Get current menu_order

If you have the post with an $id:

$thispost = get_post($id);
$menu_order = $thispost->menu_order;

WordPress itself does not provide a function to get the menu_order, so you have to query the post-Object. If you are outside the loop, you can use the above function, however inside the loop you could also achieve this by:

global $post;
$menu_order = $post->menu_order;

The Menuorder is mainly used for Database Queries, as the Name says, do determine the Order of the output (if the menuorder is selected to be the order criteria).