It is no possible to edit a structure from the web content editor.
Steps to reproduce the problem:
1) create a simple structure + template
2) create a web content for this structure + template
3) when in the web content editor, try to edit the structure (sheet with pencil)
4) the structure editor will open and you can change the structure (e.g. simply change the label of a field)
5) now try to save the structure
6) popup "Editing Structure Details" will show up, click on the Save button in the popup
7) a message will be displayed in the popup: "Waiting for an Answer" (cf see attached screenshot)
After a couple of seconds the message goes away but the popup still remains opened. The structure has not been saved.
Workaround: You have to edit the structure in the Control Panel -> Web Content -> Structures.