An excerpt from http://www.sitepoint.com/wordpress-categories-explained/, by Jérémy Heleine
Organizing WordPress posts into different categories is essential if you have many posts. That way, your visitors (and you!) can easily search and sort your posts and only see what they want.
In this article we’ll look at how we can manage WordPress categories. We’ll begin with the description of some basic things about adding, editing or deleting a category.
Then, we’ll look at how to display a list of our categories, and how to customize this list, with the default widget that WordPress provides us.