The default categories widget provided by WordPress includes all the categories of your site. To exclude some categories from the list you need to apply a custom filter using a series of IDs.
Just insert the following code into your functions.php
file:
function exclude_widget_categories($args) {
$exclude = '2,4,6'; // Category IDs
$args['exclude'] = $exclude;
return $args;
}
add_filter('widget_categories_args','exclude_widget_categories');
Now the categories with ID 2, 4 and 6 won't appear in the output of the widget.