Yes, you pretty much figured it out. It’s basically the absolute position of the surface point being currently drawn with that material. And yeah, since it’s done for every pixel, it can potentially run millions of times per second. GPUs are that crazy.
To expand on your experiment: the reason it looks fully white or fully black is because the values are in world units (so they are obviously much greater than 1.0 for positive and less than 0 for negative coordinates). When you divide it by the object radius, you created a gradient by making all surface points inside the object radius fall into values between 0 and 1.