From wordnik.com: n.
In biology, the science of the metamorphoses or changes which an individual undergoes from the time it ceases to be an embryo to the time it ceases to live as a bodily organism,
For me, meta-morphology involves meta. Best I can tell, meta = self-referential. My favorite example is:
I'm so meta even this acronym.
(I couldn't figure out to whom to credit this, so if anyone knows please tell me in the comments below.)

So, for me, Metamorphology is:
The study of self-referential change.
You go out, live your life and experience new things and get exposed to new ideas. All of this is interpreted based on what you've previously experienced or been exposed to. The integration of the new information either changes you or not. How resilient are your belief structures to contradictory experience/ideas? Are there ideas or experience that can affect that resiliency? How does one's belief structure resiliency inhibit or facilitate someone's metamorphosis?

Metamorphology is an attempt to understand how this process works, from somewhere between neuroscience and spirituality.