The charges in the center want to get away from each other. They jump off the sphere to get farther away from the other charges. The gas inside the Plasma Ball glows where the electricity passes through the air. The charges are trying to go where there is no built up charge. The sphere builds up charge really fast because it's small.
Charges always take the shortest, easiest path.
If your friend lives next door, you wouldn't walk around the block just to go to their house. It would be easier to just walk straight there. Keep anyone with a heart condition or pacemaker away from all our electricity demos. It's not dangerous, but it can be startling. Leaving your hand on the sphere in one place for a long time generates heat.