This tutorial covers the Delete Category fields after clicking on the the admin's right nav links. If you wish to delete a cateogry, you will need to delete or move the products from that category to another category.
1. Select Category - Chose the category to delete from the dropdown list.
Once you've chosen a category to delete, click the "Submit" button. You will get an confirmation dialog to confirm deletion of the category! Click yes, to delete, no to cancel.