Looking at that image, I am wondering if the phone is in it or a browser or app is in it. I have heard of a lot of modes, but never called that. Have you tried the following...
1. If only happening in one app, closed the app, restarted (powered off and back on) the phone and tried entering the app again?
2. If happening on the phone itself (any app) then try and swipe down from the top of the screen and in looked to see if there is an option to exit it.
3. Should that not work, and a restart (power off and back on) not work, then try starting in "Safe Mode" and see if that changes it. (Instructions below)
If it shows fine in "Safe Mode" then there may be a bad app, virus or malware on the device which will have to be found and removed. If it still says that while in "Safe Mode" then you may have to "Hard Reset" the device.
To get into "Safe Mode" please do the following.
1. First turn off the phone.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.
You can't back up everything. Which I stated before. The best you can do is either upload what you can back up to a google account or other cloud account, or connect to a computer via USB cord and move all the files you wish to save (contacts, etc.) onto the computer.