The object pivot is the position about which objects are scaled and rotated when playing back animation. You can change and animate the object pivot, such as for creating a rolling cube.
Because you cannot directly animate the transformation of an object's center, you often create a null, parent the object to it, and then animate the null (see Animating the Transformation of Object Centers [Animation]). This is a quick and easy way to work for effectors in a skeleton or other objects, but for bones there is a problem. The bones in a skeleton hierarchy cannot be cut from their parent object so that you can insert a null and parent the bone to it. Using the object pivot, you can offset and animate the bone's pivot regardless of its parenting.
For information on using and animating the object pivot, see Working with Object Pivots [Working in 3D Space].
These are some other possible uses for pivots in skeletons:
Create a foot roll rig by constraining an effector to a null and animating the null's object pivot. Using pivots means fewer nulls in the rig, which makes for a less complicated setup that's faster in performance and easier to animate.
Animate the object pivot of an effector for creating cycle movements with IK, like bicycling. You can also change the pivot's scaling to create more elliptical cycles.
Change the rotation of a bone's pivot without changing its axis alignment (see Changing the Bone's Axis Alignment for Mocap Data). This way, you can rotate the bone on any axis you like without having to reset each bone's actual axis of rotation.
