Is this the blog you are talking about http://billeger.wordpress.com/ ? If so, you can create categories when you write posts (add category from the categories section) or you can create categories from the posts > categories page. Categories will only show up on your blog in the categories widget when they have been assigned to at least one post, and that post has been published.
If the categories showed up in the sidebar when no published posts had been assigned to them and someone clicked on a category name, then there would be nothing for the software to show the visitor.
Create your categories, write posts, assign categories to them and publish them and the categories will show up.