Apperception and die Einheit, unity

While reading Kant's transcendental deduction in the Critique of Pure Reason, it is helpful to trace the use of the word die Einheit, "unity" to try and explain the origin of the necessity for the idea of apperception. That is, by tracing how the word "unity" works, we can see really what Kant means by "apperception."
Kant in Section II of the Transcendental Logic is summing up what he has proven about the necessity of synthesis. He explains this by saying that "we cannot represent anything as connected in the object without having previously connected it ourselves" (Critique of Pure Reason, Everyman edition, p. 98, [B129]). The things that are represented to us, would appear as completely unrelated and contingent if they were not, prior to their representation to us, connected. That is, like Hume, we would not be able to see any necessity between something like cause and effect: an event A would be represented to us, and an event B, but we would not see them related. Hume ascribes this relatedness to habit only. Kant objects: if something is to be related by habit, it must be possible for the things to be related or connected by thought. In other words, two things cannot be related or connected at all by habit if thought cannot relate or connect them.
This connecting, prior to representation, that gathers together or ties or binds together (verbinden) "the manifold of [individual or singular] representations" ("das Mannigfaltige der Vorstellungen"), is synthesis. This "previous connection" of representation, however, "cannot be given through objects." Why? Well, because objects produce only representations--this is what Kant means by "sensibility." Objects can in a sense effectuate connections between them, but these connections are not able to be represented purely through sensibility. We are concerned with the represented connections between objects only. An object's connection with something would only just be represented as another singular representation. We are concerned with connection between representations, which happen in the subject apart from the object. This connection, then, is "originated only by the subject itself, because it is an act of its purely spontaneous activity" (98, B129), that is, activity free from the influence of objects insofar as their representability as connected is concerned. Let's look at the word "spontaneous," however, a little closer.
Kant uses two words to describe this connecting act of the subject, but they both only get translated as "spontaneous," (one, indeed, gets translated as "pure spontaneous," but this is highly inadequate). As we just pointed out, it is obvious that Kant is using it to describe how the activity of connection or binding together of representations occurs in the subject--i.e. that it is impossible in the object. The first word is closer to "spontaneous," in the sense we are articulating here--that is, free of influence: Spontaneität. Kant says, "denn sie ist ein Actus der Spontaneität der Vorstellungskraft" (B130), "then it is an act of spontenaity of the faculty or power of representation," a moment when the power of representation has free play, is unencumbered by the existence of the world of objects. That is, the power of representation is indifferent to the existence of the object, since the representation of it is given only insofar as the play of the power of represenation can take it up--and if it has taken it up, it already must exist, so the concern of the power of representation with its existence has already taken place. It is now free to do what it wants with the object as represented.
But the second word Kant uses is stronger, and more revealing of where he will go in this passage. Kant says that the act of the power of represenation here is Selbstätigkeit: "weil sie ein Actus seiner Selbstätigkeit ist", "because it is an act of Selbstätigkeit." Literally, it means self-acting. To us, the word means something more like "free play," which we used above, but still with reference to not being encumbered by an object--free play in the sense of automatic, automaton, automatisch, unfolding of itself. That is, this "automatic" should be taken in the sense of "autonomous." Put better, Kant means here that the act of the connection of representations prior to representation, synthesis, is an act not just totally free of concern for the existence of the object of the representation, but is generative of the subject which will receive the connected representation as such. It is autonomous in the sense he uses this word in his Groundwork for the Metaphysics of Morals. It is the act of the self, this self-acting unfolding of the free-play of this faculty of represenation: in other words, the self comes out of or results from this act of connection.
This is important to note because we suddenly see where Kant is going with this--it makes his next point seem less strange or foreign.
Kant suddenly says "But the concept of connection includes, besides the concept of the manifold and the synthesis of it, also that of the unity of the manifold. Connection is the representation of the synthetical unity of the manifold." (98, B130-1). What Kant really says here, in an extremely complicated way, is that the act of representation prior to represenation, the connecting of the representations in synthesis, is not just the mere connection of individual or singular representations prior to the representation of that connection. It is also, and actually primarily, the activation or bringing-into-actuality of the prior potential for unity inherent in the representations themselves. That is, Kant is laying the emphasis on the capability of unity that these representations must also already possess as a possibility in order for them to be eventually connected or bound together at all. Connection is the representation of synthetical unity of the manifold (of representations): the accent falls on this unity.
The question becomes, then, where does this unity come from? Because, as Kant remarks, it "therefore cannot arise out of connection" (98, B131). In other words, this unity, die Einheit simply means the possibility of connection at all, because it is what in the manifold of representations is not just a manifold of individual representations, but a manifold of individual represenations that can cohere or unify, can simplify (vereinfachen) into a representation. And insofar as it is this possibility, conceived in its purity it is not yet related to the eventual connection of representations into one representation itself (through synthesis). Rather, Kant quickly shows us that connection must originate from this unity, this possibility: "much rather does that representation by adding itself with the representation of the manifold, render the concept of connection possible" (98-99, B131). The possibility for a connecting synthesis, this "unity," is the real determining factor for anything that will be represented to the mind.
And we have to understand that, for Kant, this is really where the power of representation, the whole process of eventual synthesis and connection of representation, originates and is at work--but not yet as itself. In other words, connection as an act is really located here, in the unity: connection itself just issues forth from this act of unifying that is not yet action, not yet reducible to the power of representation as such.
This is why Kant calls by another name "apperception." We can also see this act within the unity prior to the connection of representation is really just the act of positing "I think." Because we saw how Kant uses the word Selbstätigkeit, we can see that it is this aspect of the power of representation that gets accented in this unifying act. In other words, we see that it is this aspect of the power of representation taken purely and alone, the self-action of the self-acting power of representation or synthesis. This is what we meant by saying that this self-action generates a self: the generation of a self in the "I think," is what occurs in this unifying. Why does it do this in this unity, however? Why does this generation of a self take place within the unity that makes possible the connection of representations?
Because, as Kant explains, and as we put it above, this unifying is the prior possibility within the multiplicity or manifold of representations to be eventually connected into a representation: it is the reduction of a manifold to a one. This one, for Kant, simply is the perspective of the subject. In other words, what is happening is that Kant says that the unity that makes possible the connection of representations lies in how there must be a way for the manifold of representations to cohere into one perspective. Thus this unity is the site or rather the pure action itself of the generation of the subject, of the self.
Anyway, I hope this was a little helpful in explaining some tough phrases within the Critique and how they work. One can figure this out simply by paying attention to the architecture of the mind as specified by the faculties, but it is more useful and ultimately more productive to investigate how and particularly why Kant needs them to work the way they do. Apperception is the question of whether and how the subject, as asubject, can exist at all, and it is only by seeing that this is the function of apperception--guaranteeing the existence of a subject--that one really understands what Kant is doing. This is why people stress this section in Kant, and, as we can now see, why it ultimately is considered a rereading (and an absolutely genius one) of Descartes. If objects do not end up representing themselves to a single subject, that is, if they do not become determined by an act of the mind asserting itself as singular, as one perspective, prior to their actual representation, there could be no representation at all, or at least any representation we would be familiar with and call a subject.