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That screen indicates that the firmware/software of your iPhone is corrupted during the update. Your only option is to force-restore the iPhone to factory settings through iTunes application (from computer) which will erase everything from it.
But if you've backed up your iPhone to iTunes on your computer or iCloud, then you can restore all your data back after restoring your iPhone from iTunes/iCloud. You can also redownload all your past purchases for free using the same account.
Follow the steps below to restore your iPhone by putting it to DFU Mode.
First download and install latest iTunes on your computer from here : https://www.apple.com/itunes/download/
Then connect the iPhone to your computer with the USB Cable.
Open iTunes application on your computer.
iTunes will ask you to restore the iPhone.
Click OK or Restore
Remember, it may take a while to restore the iPhone (the iOS firmware has to be downloaded, you will see the Download button - a downward arrow button with spinning circle around it, at the top right corner of iTunes screen. Click it to see the time remaining)
Please let me know if that didn't work, so I will continue to help you until we fix the problem.
We can continue later. Add a bookmark of this page or add this page to your favorites. So we can continue later or any time you want.
When you are back, you can follow the steps above to restore the iPhone to working condition. You can restore it from any computer.