If at any point you deviate from the prescribed route, Google Maps Navigation will automatically find a new route using your current location and direction of travel. When this happens, Rerouting will show in the header and voice instructions will stop temporarily until a new route has been found.
For Android devices, rerouting does not require an active data connection. If you lose your data connection, you can still use automating rerouting.
For iOS devices, rerouting requires an active data connection and access to your location. If you lose your data connection, you'll need to wait for an active connection before you're rerouted.