Hello Peter. Thank you for your question. Well, it's exactly how you put it: just how does the hardware implement the software? In computers, software is just a pattern of hardware. That's an identity statement. In the mind-body debate, the prevalent belief is that neural patterns just are mental states/phenomena. That's also an identity statement, but can be couched in more sophisticated language like supervenience theses of the relation between the two. Most theories of mind, like functionalist ones, accept some sort of supervenience relation, except maybe for some strands of emergentism. To my mind, I easily grant the truth of supervenience, but not only is it not sufficient for physicalism, it has zero explanatory power. What's unclear, or what we don't know, are the mechanisms by which the brain realizes mental phenomena. The computer metaphor may be correct in a broad sense, but probably wrong in any narrow sense: the causal relationships between a brain and a mind, if we can talk in terms of them being separate, which we can't without ipso facto creating conceptual dead ends, are probably not quite like the causal relationships between software and hardware.
What terms are explanations of software functionality usually cast in?