Yahoo Mail does not skimp on user-friendly email organization tools. The left sidebar where you previously added new folders is also where you delete them.
Empty the Folder Before Deletion
Yahoo Mail doesn't allow you to delete a non-empty folder in case it contains emails you want to keep. To delete or move an email out of the folder, click the check box next to the message and then "Delete" on the main toolbar above the message area, or click "Move" and select another folder. You can also remove all emails at once. Select the check box at the left end of the toolbar and move or delete as needed.
Select the Option to Delete
Although Yahoo Mail displays most of the tools you need on the toolbar, tools for modifying the sidebar are available only through hidden icons and context menus. Yahoo also allows you to delete only one folder at a time. To perform a deletion, position your cursor over the folder's name, right-click to reveal an options menu, select "Delete Folder" and then click "OK."
Use Mail Folders More Efficiently
Instead of deleting a folder, consider how you currently store your email and consider using the folder for a new category of stored messages. The context menu offers an option to re-purpose a folder so you don't have to waste time creating new folders as your needs change. Click "Rename Folder," type the new name when prompted and then press your keyboard's "Enter" key to save the change.