Exports your database, does a find and replace on URLs and file paths, then allows you to save it to your computer.
I just tried this with wordpress 3.8.1. I got it to install fine but then it just produced an empty page when I tried to export the DB. Did not work in Chrome or Firefox or even IE.
I am on a shared host with a 60 second script limit so maybe the plugin cannot deal with this.
Support was very responsive and nice, but not helpful. Copied site just did not work. It does not matter whether I updated my permalinks and all the other stuff: Start page showed up, but no other link worked.
At the end, I did all the copy manually and this worked :)