First I will explain what the issue here. Your iPhone was automatically updated. There is a feature called 'Find My iPhone' that was activated on your iPhone prior to the update. This is an anti-theft measure by Apple that blocks unauthorized access to your iPhone . Since the software is updated and Apple detected a change in software, your iPhone is now asking you to verify that you are the original owner of it. So you need to enter your Apple ID/iCloud and password ***** activate it. You will not be able to use the iPhone until you activate it.
Apple ID/iCloud ID would be your email address you registered with your device.
If you don't remember the password, then you have to reset the password. You can reset it from here (go to this website from your computer) --> https://iforgot.apple.com/
Go to the above website. Use the "Get an Email" method to reset the Apple ID. Apple will send the reset instructions to the recovery email you setup with your Apple ID. It would be your email registered with Apple, like Gmail, Yahoo etc. Open your email and you will see the email from Apple. Open it and follow the instructions to reset the password.
If that didn't work, then go to this site again --> https://iforgot.apple.com/
This time use the "Answer Security Questions" and answer the security questions there to reset your password. Then use your ID and new password ***** activate your device.
If you don't remember your Apple ID, then you can find it from
here --> https://iforgot.apple.com/password/verify/appleid#!§ion=appleid
Please let me know if that didn't work, so I will continue to help you