Crystals are a tool used by Jareth along with his magic powers. He is typically seen twirling one or more around in his hands. They hold much power when in his hands, including the ability to change form and cause hallucinations. He can also view any part of the Labyrinth, and possibly outside as well, using these crystals.
Jareth offered such crystals as gifts to those he desired. The last crystal he would ever posess was offered to Sarah. The crystal popped like a bubble when she remembered the magic words that would bring Jareth to his end.
The crystal ball manipulation in the film was choreographed and performed by Michael Moschen.