The terms subject and object have a very complex history (the terms have opposite meanings in classical and modern philosophy). For the purposes of this question, I'm going to restrict myself to the modern usage (as we find it in Kant and Hegel).
The basic concept is that there's a subject (let's say a self) and this self faces many particular things in its world, which it encounters as objects. The etymology of object [both the Latin Object and the Germanic Gegenstand] is something that stands against the self.
There are many different accounts of how selves then relate to their objects, but your phrase
subsumption of things into selves is actually pretty spot on for an explanation Hegel uses in Encyclopedia Logic, Phenomenology of Spirit, and Philosophy of Right to describe how the self interacts with objects.
There's a hierarchy like this:
- there's an animal conception where the animal subsumes the object by consuming it. Here, on the basest level, everything is an object for that self to eat.
This is supplanted by a more advanced conception where the self comprehends an object -- subsuming it without consuming it, which Hegel considers more advanced. Everything in the world is brought under the categories of the self (Kant is still on board for that and in a weird way so are thinkers like Aristotle and Aquinas).
Hegel draws from 2 an interesting idea -- that the most interesting thing going on in thinking is the activity of the self in thinking.
Maybe to reword that, a dog eats, an unthinking human person encounters objects in the world and puts them in categories, and a thinking human person thinks about his categories and the contours of his thinking. (Here's another version appearing in Hegel's Lectures on Proofs for the Existence of God see esp. p. 276 -- in this version, the move is to recognize that the contingency of things is bound together by the necessity brought by Spirit [self and thought]).
Thus, for Hegel, there's a deep connection between social life and the self. To understand this, we need to merge the account above with an interesting section in Encyclopedia Logic (also in the longer logic) entitled "The Object," which looks at how the sorts of objects we encounter in the world and how we encounter them. Hegel believes these objects can really be divided into three categories: physical objects, chemical objects, and social objects (things split into these categories based in part on the sort of rules through which we understand them).
Physical objects follow physics. Chemical objects the rules of chemistry (as Hegel understood them). Social objects follow social rules. And in each of these, it's not to just something out there but rather something we contribute to the objectification of. To give an example, I can consider water as either a physical object (pressure drill?) or chemical object (solvent?) or social object (holy water? Ganges river? sign of purity? sign of peace?). Social objects, for instance, marriage do not have a physical thing to point to (in the absence of children) that constitutes the marriage, but marriages exist.
Regarding the reverse "subsumption of self into things," Hegel is going to deeply opposed to this, because again for Hegel the prize is to bring everything under thought with all of its distinctions.
Regarding subject, object, and human history, we can reconstruct it from the details I've supplied above, but for Hegel, the story of human history is the discovery of objects, then the discovery of subjects as on the other side of objects, then the discovery of the subject as that which thinks about objects, and finally as thinking itself... (this is Hegel's progressive arc of history).