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The "wp_nav_menu_args" filter is applied to the arguments of the wp_nav_menu() function before they are processed.

This filter can be used in the child theme's functions.php to add/remove/modify the arguments of a menu defined in the parent theme.

Also, plugins can use this filter to change menus by adding classes/IDs or using a custom walker object.

Example with Twenty Thirteen Theme

The Twenty Thirteen theme defines the following menu in its header.php file.

<?php wp_nav_menu( array( 'theme_location' => 'primary', 'menu_class' => 'nav-menu' ) ); ?>

The following example code will add an ID to the container and change the "depth" to -1 so that links at all levels are displayed in a single, flat list.

function modify_nav_menu_args( $args )
{
	if( 'primary' == $args['theme_location'] )
	{
		$args['depth'] = -1;
		$args['container_id'] = 'my_primary_menu';
	}

	return $args;
}

add_filter( 'wp_nav_menu_args', 'modify_nav_menu_args' );

The container ID will only show up if you set a menu for this theme location.