"Airplane Mode" is designed to turn off all the radios on your cell phone. That's what it does. The reason behind this is that (until recently) the FAA required all radio frequency emitting devices in the cabin be turned off during flight, and particularly during the critical phases of taking off and landing.
These restrictions have been relaxed, to a certain extent, though many airlines still ask you to turn off or put into airplane mode your devices prior to takeoff or landing.
Once you are in airplane mode, you can selectively turn on your WiFi and/or Bluetooth.