To delete a Library Folder, click on the Folder that you would like to delete, then click the Delete button in the top right corner of the page.  

A window will appear asking you to confirm your decision to delete the Folder and its contents.  To delete the Folder and its contents, select the "I wish to delete the Folder and all its contents" checkbox > Delete. If you do not wish to delete the contents in the Folder, you'll click Cancel, and move the contents to a new Folder. Once you move the files to a new Folder, you can then delete the old Folder.