"If you're signing in from a different location than you usually do, we may ask you to enter a code from the Google Settings app on your Android phone or tablet to make sure you own the account. You don't need an internet connection or phone/SMS connectivity to get codes using this app."
The Google Settings app is the UI for Google Play Services, Google's framework that delivers new features and APIs without installing a new Android version. It has nothing to do with the built-in Settings app, which is part of the operating system and can't be updated by Google.
The verification code has 8 digits and it can be obtained by opening the Google Settings app, tapping the menu button and selecting "Get verification code".
