How do I "Approve my iPhone" for ios 10.2?
From what I have gathered in my own frustrating search tonight is that without any other apple devices you have to select "can't activate this phone" from the bottom and you will lose only your saved passwords in keychain, meaning if you don't remember them you will have a not so fun time resetting those that were forgotten, but if you're not concerned with losing your keychain passwords then don't worry nothing will change. 

For those of you who stumble across this issue and have a MacBook which doesn't get a pop-up window, (my situation earlier) go to your settings on your MacBook and find keychain under iCloud preferences, it should say iPhone is waiting for verification. Click this and enter your apple ID and it should activate your phone.