Backup only backs up your personal data. All of your apps are saved on your computer, and will sync whenever you Sync after.
My last post was confusing. Let me set it like this:
1. Before you do anything, sync you iPhone with iTunes to create a backup. After a full sync, go to Edit>Preferences>Devices. Make sure that a backup was actually made.
2. Follow the tutorial. When it says to "Restore" and the beginning, they want you to clear everything off the phone. This is so that any of your apps and things don't mess with the Jailbreak process. On iTunes, click Restore, and after a few moments, when it asks to restore from a backup, DO NOT choose your backup.
3. Immediately following the restore, your iPhone should be as if you just got it. Follow the rest of the tutorial.
4. At the very end of the Jailbreak process, you should end up with "Cydia" and/or "Installer" on your iPhone. Your iPhone is jailbroken!
5. Open up iTunes and click "Restore" again. This time, after it a few moments, choose your last backup.
6. After your phone is backed up, Sync as normal.
Sync - Puts all your music, apps, media, etc.
Backup - Puts back all of your personal data.