If you want to edit your categories and sections or delete them altogether, you need to open their settings by clicking the corresponding icon next to the category in question. This icon appears by mouse hover.
You can change your categories and sections' names by double clicking on them. Make necessary changes and press Enter to save them.
This menu contains fields for changing your category's name, its description and slug (last part of the URL after /). This is where you can delete the category completely by hitting the corresponding button.
You can also open the Advanced Settings to specify SEO and social media settings for your page:
In this menu, you can rename your section, move it to other category or delete it: