Obviously, the use of Titanium is for backups. One plus of having Titanium for root is that it backs up your data as well as your app, meaning all of your progress/settings are saved when you restore. To backup an app, go into the second tab (backup/restore), tap on an app, and press back up. You can also go into batch actions (top right button with check mark) and back up all of the apps in one go (pro version only)
A NOTE ON WHICH APPS TO BACK UP
As you can see, titanium also has color coding, giving you further details on each app. To see what all the colors/symbols mean, go to
Menu --> Help/licensing --> Legend
As a beginner, it is best that you simply stay away from all red apps (system apps). Chances are, if you are flashing a new version of the rom, it will be included. The green ones should NEVER be restored on different roms, but can be used on different versions of the same roms. It is essentially all of the rom settings in files. Yellow ones are typically text messages or wifi networks and can always be backed up or restored, as they are simply xml files. Regular apps (user apps) can always be backed up and restored.