Don't let the name "Firefox" fool you, because Home isn't really a web browser. It works in concert with the Firefox sync add-on for the desktop. Once you've got that installed and created an account, you'll launch the iPhone app and re-enter your credentials.
The app will remember what tabs you had open most recently and present their contents to you. You'll also have access to your bookmarks, recent browsing history and web search.
The service syncs 2,000 of your most recently visited items every 24 hours, and new data is synced every time you launch the app. Good luck to the Firefox Home team. We hope to test your solution soon.