The Subject
The grammatical subject is a conventionalized principle, which a community decides to impose on itself because speakers do not always specify what it is that they are talking about.
Again from The Instruction of Imagination:
Functionalists claim that the syntactic notion of subject can and should be defined in terms of its communicative function—as the topic of the sentence, what the sentence is about, and as its most prominent argument. Generativists contend that this is sometimes true, but not always, and it is definitely not true when the subject seems to have no semantic significance (when it is expletive). Thus, in the English sentence "It is raining," the subject it is not what the sentence is about, simply because it is very unclear what it stands for in the first place. . . .
The subject cannot be defined as a function from the private experience of aboutness to a certain structural configuration, for the simple reason that it appears in situations where the experience is not there. Once again, to resolve the problem we have to reverse the order of things and look at the subject not as a natural function from experience to language, but as a prescriptive function—from language to experience. The contention that the subject is what the sentence is about should not be read as a description of something that is simply there, but as a conventionalized, regulatory principle, which a community of speakers decides to impose on itself precisely because the speakers of the community do not always naturally specify for their listeners what it is that they are talking about. A prescriptive principle, through which the members of the community (acting as listeners) tell themselves (as speakers): "From now on, whenever you tell me something, make sure that you remember to tell me what (or who) you are talking about. It will help me understand."
P.S.: Find out more about the famous buffalo sentence here.