WordPress at a glance
function is not described

_update_blog_date_on_post_publish() WP 3.3.0

Handler for updating the site's last updated date when a post is published or an already published post is changed.

No Hooks.

Return

Nothing (null).

Usage

_update_blog_date_on_post_publish( $new_status, $old_status, $post );
$new_status(string) (required)
The new post status
$old_status(string) (required)
The old post status
$post(object) (required)
Post object

Code of update blog date on post publish: wp-includes/ms-blogs.php WP 5.2.1

<?php
function _update_blog_date_on_post_publish( $new_status, $old_status, $post ) {
	$post_type_obj = get_post_type_object( $post->post_type );
	if ( ! $post_type_obj || ! $post_type_obj->public ) {
		return;
	}

	if ( 'publish' != $new_status && 'publish' != $old_status ) {
		return;
	}

	// Post was freshly published, published post was saved, or published post was unpublished.

	wpmu_update_blogs_date();
}