In my limited experience (which pales in comparison to, for example,
@osakajoe 's), "a good heat treatment" can be used to describe any the following features (often in combination, but there are tradeoffs between some of these):
1) Good sharpening feel and feedback (for me, it's especially about steels which feel smooth or creamy to sharpen and steels which give feedback about when you are sharpening the edge).
2) Ease of sharpening (how quickly/ easily can you grind the steel)
3) Ease of deburring.
4) Ability to hold a fine polish.
5) A steel which feels hard on the stones (which may be seen as giving poor feedback to some People).
6) Long edge retention.
7) Good edge stability (will hold a fine edge).
8) Adequate toughness.
I'm guessing that a fine grain structure probably contributes to ease of sharpening, sharpening feel and feedback, ability to hold a polish, toughness and possibly ease of deburring.
A high hardness contributes to edge retention (but probably less than the carbide structure), edge stability and a hard feel on the stones. Probably also to ease of deburring. It may or may not affect sharpening feel (there is probably a hardness sweet spot as very soft steels can feel gummy), toughness (once again, there are sweet spots) and ease of sharpening.
A good carbide structure probably contributes to the feel of hardness on the stones and is important for edge retention but may reduce edge stability (depending on carbide size). It probably affects toughness but I suspect in a complex manner.
Note that there is some degree of tradoff between a fine grain structure, carbide structure and probably hardness in the heat treatment process. A good heat treament is probably about finding an acceptable tradeoff between these which meets the intended charecteristics of the knife.