Go to your header file(header.php) and here you will find a function wp_nav_menu($args)
So if you did not want to show the navigation bar than you can remove the php script through which this founction is called and finally you will get the desired result as shown in the image below(no navigation bar)
In some cases function wp_page_menu($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.