Most of the folks I know that use the model just look at the comments in the code to make the understanding.. but of course most of them STARTED with opamp macro models in spice.. (probably showing my age) so we don't need more..

Basics - first stage sets the gain, accounts for input saturation.
second stage sets the dominant pole
output stage takes into account the supply clamping, output loading (by way of feedback to the second stage)

This is off the top of my head.. hopefully others can expand on this..

its (or something quite similar) is probably described in Miller and Fitzpatrick as well... but this was probably not copied from that ..