Go to your header file(header.php) and here you will  find a function wp_nav_menu($args)

This function Displays a navigation menu created in the Appearance → Menus panel.

So if you did not want to show the navigation bar than you can remove the php script through which this founction is called  and finally you will get the desired result as shown in the image below(no navigation bar)

Header with no navigation bar

In some cases function wp_page_menu($args) is used in header file in order  to show a  navigation bar.

wp_page_menu($args) # Displays a list of WordPress Pages as links, and affords the opportunity to have Home added automatically to the list of Pages displayed. This Tag is useful to customize the Sidebar or Header.

Similarly you can erase this function fro the header file to remove the navigation bar.