In Catalog -> Categories, you will see a tree list of categories if you have already defined categories. Click the category that you wish to delete. You will be shown the detail about the category and action buttons on the bottom. If you don't see "Delete Category" button it's because there are products in this category. You cannot delete the category that are having products. You have to delete the products in the category first. Click "Show Products in Category" button and you will be shown a list of products in this category. Remove all the products and then go back here. You should find the "Delete Category" button. Click the button to delete the category.