Your reward is 60 Gems for each set of targets you complete, with 60 more being awarded for nailing them all in one run. Your run is over when you either run out of time or destroy all the targets in the level. Destroying a target object will give you a few seconds more time added to the clock.
The object is to fly about and destroy all of the target objects in the level before time runs out. With one exception, Flight levels are the only levels in the game where Spyro can actually Fly rather than just Glide.