Freestyle is the most expressive and beautiful of the Frisbee disciplines. It evolved from the simple game of throw and catch and now includes aspects of dance and gymnastics as players perform tricks, turns, and seemingly impossible catches with the Frisbee. In the overall, it is a pairs event where teams perform with music in front of judges who rate the routine based on difficulty, artistic impression, and execution.
Instead of trying to explain freestyle, I recommend you experience it. There are dozens and dozens of amazing videos of freestyle put together by the
Spread the Jam project.