This ball is weighted at one pole so that if you throw it by applying a force at any other point, it wobbles as it flies through the air.
The center of mass of an object is the weighted mean displacement of all of its mass points from some reference point, usually the origin of the coordinate system in which the object sits. This is the sum of the products of all the mass points with their distances from the origin, divided by the total mass of the object (rcm = Σmiri/M). If we set the center of mass of the object at the origin, we find that this sum equals zero. This tells us that if we exert a force on the object at its center of mass, this results in no torque on the object, but if we apply a force to the object at any other point, we exert a torque on the object about its center of mass. The center of mass also has the interesting property that, when a force is applied to the object, its center of mass moves as would a point mass, equal to the total mass of the object, subject to the same force. That is, no matter what the overall motion of the object is, its center of mass follows a simple path. For example, if the object is tossed up in the air from one place to another, no matter how the object rotates or twists, the center of mass follows a simple parabolic path.
The ball in this demonstration is an interesting one. It is a “Guac” ball (made by Creative Imaginations, Inc.), which is an inflatable ball that has at one pole a pouch of sand, which puts the center of mass of the ball very close to that pole. If you set that pole on your hand and then toss the ball in the air, its motion is fairly simple. The ball follows a parabolic path, and does not do much else. If, however, you place your hand elsewhere on the ball and throw it, as you do so, you exert a torque on the ball about its center of mass, and as the ball flies through the air, it wobbles dramatically. The pole itself follows a simple parabolic path.
References:
1) Resnick, Robert and Halliday, David. Physics, Part One, Third Edition (New York: John Wiley and Sons, 1977), pp. 162-168.