I'm in the process of installing this myself. I have run into several problems running my joomla sites here locally on my computer using wamp (especially the templates) and they run fine on the production server.
From what I understand, my site will be running in a Linux environment as if it were installed on the actual server so I will be able to develop my site as if it were on the server without any problems. This is the solution that I need when I'm developing a site. That way I can create everything on my computer 1st and then put it online once it's complete. If you want to run your site exactly as if it were on the server then I recommend you to do this. I will let you know my results once I get everything installed and configured. 38% downloaded...

Yes, that's correct. The JumpBox allows you to run a local instance that's a fully self-contained, pre-configured system including everything (OS, db, web server, app server, application, dependencies). Being able to develop locally and offline is one of the benefits. Another is as @bbefox pointed out, the portability. You can fire up a Jumpbox in a hosting environment and use the backup/restore feature of the admin to move your instance live. It's a simple way to develop and deploy and know that everything will work since it's identical from the ground up.