At this point, your iPhone will connect to your phone company's servers in order to verify your account and continue the set up process.
Follow the onscreen instructions to confirm your phone number. Once that's done, you'll need to enter the billing zip code on your account with your phone company and the last four digits of your social security number.
When you tap the Next button, your phone will check in with the phone company's servers to move your service and phone number over to the new phone. Wait for the activation process to complete onscreen and you'll be taken to the next step.