GPS is a receive-only technology. There are satellites in orbit around the planet and these satellites transmit. Your device receives these signals, but does not communicate back to the satellites. Using your device with GPS is no more dangerous than using it without GPS.
Airplane mode is basically equivalent to "turn off transmitters", though you can also reenable WiFi and Bluetooth. Using GPS is completely consistent with transmitters being disabled.
Assisted GPS is a way of improving the time to first fix. Your device communicates to local non-satellite infrastructure (a cell tower) and receives information about what satellites are currently in view for the local area and orbit corrections. Satellites also communicate this information, but it is much faster to receive this from a local data connection. Without assisted GPS, your time to first fix may be ~12.5 minutes (obviously longer if you cannot receive a good signal). With assisted GPS, this can be reduced to seconds. Once you have a fix, assisted GPS is equivalent to unassisted GPS.
With airplane mode enabled, your device will not use assisted GPS because it cannot communicate with the assisted GPS infrastructure. It will use the standalone mode. This is why people may suggest to acquire a GPS fix on the ground before you start your flight; it's easier for your device to acquire a fix with a data connection and preserve a state where you get location updates than it is to cold start in-flight.
