I found this discussion of what Hegel means by substance and subject very helpful in Karl Marx: The Early Writings, ed Lucio Colletti.
(Comments by Colletti)
Hegel inverts the relationship between subject and predicate. The universal or concept, which ought to express the predicate of some real object and so be a category or function of that object, is turned instead into an entity existing in its own right.
In other words, whenever we make a claim about something, say the ball is red, we ascribe the predicate or universal redness to the subject, the ball. Hegel takes this one step further: for him the universal (or predicate) is also a subject.
By contrast, the real subject, the subjectum of the judgment (the empirical, existing world) becomes for him a manifestation or embodiment of the idea–in other words, a predicate of the predicate, a mere means by which the Idea vests itself of reality (Colletti 19-20).
So what he is saying is that the Idea manifests itself through the subject.
We have Subject (A), in which the universal is predicate. This generates a new moment:
Subject (B). The original predicate is now a Subject. So the structure is now a Subject of a Subject. And so forth. What’s the pay off? Well, Hegel is able to show how Plato’s forms manifest themselves in history. That’s something Plato couldn’t always do.
The downside is that the Idea/Subject/Universal seems to function a lot like what we would call “God.” This would seem to mean that God needs the world (the Predicate needs predicates) to “be” God.