Start simple and work your way up.
Eject the device from iTunes and do the easy stuff; turn it all the way off and back on again.
Plug it back into iTunes again.
Check what version of iTunes you're using.
If it needs to be updated, do that first. It's less stressful than restoring your phone. Then plug it in and see what happens.
Do a fresh backup to iCloud. You'll need to connect to a good wifi network, iCloud prefers it over cellular (saving you the data, basically). Go into Settings, iCloud and log in if you aren't already. Then, down at the bottom of the screen go to Storage & Backup, then Back Up Now, again at the bottom. If the option isn't available then check FOR SURE you're using wifi.
Once you're backed all the way up Restore the phone. Like the message told us to right from the get-go...
When you're setting it back up again one of very first options is to Restore from iCloud Backup.
This isn't the type of problem that should happen more than once. If it persists after all this, call Apple.