When your iPhone is in Airplane Mode, the phone's networking and communications mechanisms are completely disabled. You can use all of the apps on the phone, but anything requiring the cellular network will not work.
Airplane Mode allows you to use your iPhone apps during flight without violating FAA regulations prohibiting the use of cellular phones aboard commercial aircraft.
Chances are, they'll still ask you to turn off or put away your iPhone or iPod touch prior to takeoff. Once you're up in the air, and they've given the "ok," then you can turn it on and play your music or games while in Airplane Mode.