The $widget_id is a string value that represents the CSS style ID for the LI that contains the widget (i.e., <li id="text-3">widget stuff</li>
… in this case, $widget_id = “text-3”). It’s not a value to change, but a value that changes based on the particular widget being dealt with by WP at a given moment. A good example to see it in action is to set up 2-3 widgets in a test site, and place the following in your functions.php file:
add_filter('widget_content', 'my_widget_function', 90, 2);
function my_widget_function( $content='', $widget_id='') {
return $content . '<p>This widget\'s style ID = ' . $widget_id . '</p>';
}
So, as you will see, each widget will contain whatever content is already in it AND at the end of each widget’s content will be “This widget’s style ID = <current widget ID>”.
HTH.