An animatable pivot is essentially a transformed objects space about which the object rotates and moves in. This transform space can have two purposes and two relatively different affects: either your object rotates/moves about an arbitary ‘pivot’ or this ‘pivot’ transforms your object -They sound the same but are different in the results they acheive.
With the first system you take into account the actual objects transform to acheive its new transform; your only keying the actual object. With the second your transforming the target ‘pivot’ object essentially pinning your object about it. Why do you need a system to handle both?
Well, in local relativity (in terms of a heirachy or closed system) the first system is key in transforming controls about a character: the ankle about the toe for instance or the chest about the hip for bending down. The second system is in world relativity, by transforming an object about the transform of another we can essentially make it a fake parent – glue it to a surface for example.
A good example of both systems in action is a skateboard move, the foot needs to be glue to the board (transforming space) but may itself need to transform about something, the edge of the board for example. Ontop of this the board itself may need to transform about the hands, to be grabbed for example.
This is why a system like this exists as another layer over the base rig, much like a pose tool is. Key generation should only be on the necessary controls and not on extraneous sliders (even if your using sliders to key them) etc unless there part of the base rig. When working in transform spaces is vitual that keys get put onto the actual objects.