Before looking at the actual essay, a brief history of the term “the subject” might be useful. In grammar, it is whatever carries out the predicate of a sentence: “I ate cake,” and so on. This is not quite how philosophers have used the term. The most relevant sense of “subject” comes from Kant. For Kant, thinking is a matter of linking intuitions (what we might call the empirical) and concepts. Intuitions just give us a mass of jumbled perceptions, and concepts, in concert with these intuitions, present us with an ordered world. The subject is what carries out this synthesis; each of our statements or perceptions can be prefaced with “I. . .”, as in “I think cake is delicious” or “I see a table.” Because this activity is carried out “behind” or “before” any actual thinking, this subject is transcendental. The important thing is the subject is universal; individual or cultural differences are accidents. Because it is a transcendental subject, that is, because it comes before experience or thought, it stands behind class, gender, and culture without being affected by them.
For Foucault, the subject is something entirely different. It is not a substance, it is not transcendental, and it is not inborn. The “I. . .” that we can preface every statement with is something that is formed under particular historical conditions by a process he calls subjectification. The engine of subjectification is what he calls power, and his basic project is to study how subjects are formed by various kinds of power relations.