This widget is designed to work on your web server, because you would not need a staging server, if you user your localhost do edit your content. So the scope of the widget is the following:
You have your normal kirby site on your server. It will be in some folder in your webroot and is setup to be accessed on your normal domain.
Additionally you would have a second installation named the staging server, which will be on another domain, but on the same server. Please see the sketched folder structure of the readme.
The Idea is, to edit the content only on the staging domain and the sync to your main site. Then, the main site would´t even have an panel installed.
It was discussed in several threads before, which would be the best way of publishing changes of the content and the code. In this widget the content is excluded from git version control, so it must be synced separately.
The command displayed in the widget is just the command, which will be executed, if you click the button.
Thoughts about your screenshot:
You can use your own shell script to sync from your local machine to your web server. This will not be covered by this widget.
Additionally, this widget will not work on Windows properly, because of the different directory separators used by windows.