The Parachute cast is a dry fly technique which affords your fly a very delicate presentation when trying to tempt those sometimes very wary fish.
My interpretation of the parachute cast is that it is simply a cast that projects your dry fly upward at the extremity of the forward delivery thus allowing your fly to float down to the water surface for a gentle touch down. Therefore, for this to be successful the dry fly on it's final delivery must approach its target from underneath the rod tip as apposed to over the top. This will give your fly no other option than to kick upward in the final stages of the forward cast and therefore float down again after the energy traveling through your fly line and leader has dissipated. An easy technique to learn.