Proper acceleration of the fly rod.
In fly casting the function of the rod hand is to accelerate the rod so that it may
load or bend against the resistance of the fly line. The hand accelerates the rod
slowly at first and continues to increase in speed until the rod reaches a position
perpendicular to the target at which point the rod hand accelerates even faster, and
concludes, with a short, ultra fast stop of the hand. The majority of acceleration
takes place near the end of the stroke.
In short: start slooooooowwwwwwwlllllyyyyy and speed up to a sudden and snappy stop.
This STOP is something Tim Raijeff talks about in this video. (the quality of the video itself isn't going to win anybody an Oscar for the best camerawork, but it well worth the watch.)