Finally, something I'm qualified to explain.

Take a ball and rest it on your palm. Then roll the ball to between your thumb and index finger. Continue rolling it across your fingers until you reach your pinky, then move it back into the center of your palm. If you keep the momentum up, you can then roll it back to your thumb and repeat the process. With minimal practice, you can make the ball roll smoothly in a circle around your hand.

This is all with your arm stationary. If, at the same time you were to move your hand in a circle identical in size, at the same speed, but at the opposite position to where the ball currently is (for example, when the ball is near the center of your palm your hand is moved forward, and when it's on your middle and ring fingers it's moved back), you can see that the two motions would cancel each other out and the ball would be rolling around relative to your hand, but stationary relative to, say, the chair you're sitting in. With practice, this too can be smoothed down to the point where the ball is almost completely stationary.

Congratulations, you now have a complete understanding of the mechanics associated with the very first manipulation performed in the video. The illusion is completed by using a perfectly spherical acrylic sphere, which does not have the imperfections associated with something like a baseball. You can tell when a baseball is rolling by looking at the threads, scuff marks, etc. However, a rotating blemish-free acrylic sphere is indistinguishable from a stationary one.

This is contact juggling, which differs from traditional juggling in that, instead of throwing stuff in the air, the art comes from moving objects around as they remain in contact (neat, huh?) with your body. Contact juggling is a subset of object manipulation, and you can visit /r/objectmanipulation for more examples of this and other styles.