mapping of menu Name "Main Menu" with variable name: primary_nav I am new to Drupal and would like to  know the details of constant/global variable:  $primary_nav 
 Observed this variable is pulling list of links from a Menu with Title : "Main Menu" . 
 I try to see the mapping of these in UI and DB, but could not find. 
Can you please help me to find out the mapping of this menu Name (  "Main Menu" )  with variable name : primary_nav  and where is it defined.
$primary_nav is template variable in Garland's template.php file. It's a variable specific to this Drupal core theme. The HTML markup is rendered by the theme_links(). 

The main argument to the theme function is page template variable $main_menu, which is defined in theme.inc. This variable is set by menu_main_menu(), which will retrieve a menu id setting then use that to look up data in the menu_links table (noted by menu_name column).