Isnt this the same thing Adobe Muse uses. I seem to recall it was using a local server?
"Isn't this the same thing Adobe Muse uses. I seem to recall it was using a local server?"
No. If you used Muse, you probably uploaded files to Business Catalyst servers. That's not the same thing at all.
"http://127.0.0.1:52073/prevew/app/index.html"
That's a temporary virtual address from Real-Time Preview. You can't copy & reuse that address because it's not real.
You don't NEED a local testing server to work with DW. But it's helpful for some things. I have WAMP server installed on my computer hard drive. And my site folder resides in the default web folder -- www. See screenshot.

When I preview in browser, the address points to my local testing server on the localhost.
http://localhost/site_name/filename.php
When you start creating dynamic websites, you will need a local testing server. In the meantime, you don't need one for static sites. But as Jon said, having one set-up gives you an alternative to Device Preview which sometimes works and sometimes doesn't.