Categories are an important part in the heirarchy of organizing your content. Articles may even belong to multiple categories.
First find an article in the control panel you want to manage.
Next locate the Categories tab.
Click on the checkboxes you want the article to belong to and they will be updated immediately.
You will now be able to find the article under the categories you have selected. If you did not select any categories or removed all of them you will not be able to find the article from within a Guide, a collection, or a category, but you can still embed the article to your site.