When you visit fargo.io the first time, on every device, you'll see a dialog confirming that you want to visit the Dropbox website to authorize Fargo, to read and write to a single sub-folder in your Dropbox folder at Apps/Small Picture. Fargo stores all your outlines, settings and status info in this folder.
Any other instances of Fargo that you have running, on your tablet, for example, observe the changes in this folder. So you could set up your desktop to have certain files open, and then when you access them from your iPad, it will have the same tabs open and they will have the same items expanded.
Note: The app folder that Dropbox creates is called Fargo for some users and Small Picture for others. In the docs we refer to it as the Small Picture folder.
One of the benefits of using Dropbox to store Fargo outlines and data files is that Dropbox automatically manages a stream of backups as you modify your outlines.
So, if you accidentally delete something, or decide you want to go back to an earlier version, for any reason, Dropbox very likely has a backup copy that you can revert to.
For more information, see the howto on the Dropbox website.