Most likely you are seeing this message because you are currently trying out a Rack Extension, and are launching Reason with your Ignition Key inserted. Since trial versions cannot be written to Ignition Key, you will need to run Reason with Internet Verification in order to access your trials.
If you choose “Continue without”, Reason will launch without your trial licenses. “Log In” takes you to the Internet Verification screen. This well enable you to access the try-licenses as well.