Pivot points control how objects rotate and scale, and also represent the exact locations of objects in space.
All transformations of an object are relative to the object’s pivot point.
The 3D manipulators also rely on the object's pivot point.
This is important because you can change the pivot point by changing the object's Center property. Changing the object's pivot point from its center alters the point around which a rotating or turning object turns. For example, a flag doesn't pivot from its center; it pivots from its edge.
See also:
Add a 3D Rotation Dynamic and Set Properties