The Discourse on the Method is a fascinating book, both as a work of philosophy and as a historical document. Descartes lived and worked in a period that Thomas Kuhn would call a "paradigm shift": one way of thinking, one worldview, was slowly being replaced by another. Descartes's work, while part of the new paradigm, still has one leg in the old mode of thought.
The old, waning worldview was scholastic Aristotelianism. The Aristotelian paradigm had a conception of the mind, of knowledge, and of science that may seem very alien to us today, but this conception held sway over Western thought for about two thousand years.
According to the Aristotelian tradition, the mind proper—what is exclusively "inside the head"—is limited to reason and understanding. Sensory perception, imagination, will, and so on, make reference to things outside the mind and so are not purely mental. Rather, they are the link that connects us to the outside world. According to Aristotle, there is no distinction between what I perceive and what is "out there." Thus, sensory experience gives us direct and immediate knowledge of objects in the world.
Science, in this worldview, is a matter of taking the immediate evidence of sensory experience and deducing certain conclusions from it. The sensory experience is indubitable, and the deductions are logical, so all scientific knowledge is based on absolute certainty.
One of Descartes's most significant contributions to the scientific revolution is his conception of sensory experience, imagination, and will as being just as much subjective mental phenomena as reason and understanding. His systematic doubting questions how it is that we can be certain about what we perceive. Descartes draws a sharp distinction between what our senses report to us and what is "out there."
This re-conception of the mind shakes the foundations of Aristotelian scholasticism. If sensory experience is no longer self-evident, then we can no longer deduce certain scientific truths from these observations. Essentially, Descartes makes us sharply aware of what goes into a scientific observation. It is not a purely neutral and objective act of seeing the world as it is; it is an interpretive act that must be undertaken with great care and circumspection.
The scientific paradigm that we have today owes a great deal to Descartes. Today, we have taken Descartes's method one step further. Now, we conclude that we can never have absolute certainty in the sciences. All we can hope for are sound theories that are supported by careful observations.
Descartes himself does not reach this conclusion. To a large extent, he is still set on finding certainty. His search for certainty, beginning with the famous line "I am thinking, therefore I exist," has largely defined the course of a great deal of philosophy since his time. We can debate whether Descartes is right in having found certainty in this claim, and we can debate what kind of knowledge this is, but it seems clear that it is not a kind of knowledge that is applicable to science as a whole. In finding this certainty, Descartes hopes to rebuild science in the Aristotelian method of deduction from certain first principles. In hindsight, this effort may seem a bit misguided.
Though his philosophy of science may be a bit askew, the philosophical method Descartes uses in part four of the Discourse has proven extremely valuable. His method of skeptical doubt has raised important philosophical questions concerning how we can be certain of, or even know, anything at all. His re-conception of what the mind is has largely defined the shape of Western psychology and philosophy ever since. His assertion that he is essentially a thinking thing and that his mind is distinct from his body has also raised a number of important philosophical questions: what is my relationship with my mind? What is my relationship with my body? If they are distinct, what is the causal connection between the two? And so on. Effectively, Descartes frames the questions that have preoccupied what we now call "modern philosophy."