Since we began life as infants, and made various judgements concerning the things that can be perceived by the senses before we had the full use of our reason, there are many preconceived opinions that keep us from knowledge of the truth.
This statement, which is the first sentence in the entire text, can be read as Descartes' call to battle. He was about to present a physics that stands in stark contradiction to everything our senses tell us, and so it was crucial for him to undermine our faith in all the sensory-influenced beliefs that we have acquired up until now as well as in the power of our senses to ever tell us anything certain. To this end, he developed an ingenious opening gambit. He asks us to throw out all of our old beliefs, to doubt everything we have ever thought we knew, and to start from scratch, building up a completely new set of beliefs based only on what is completely certain. By doing this, he is able to clear away our prejudices and open us up to his surprising and counter-sensory theory of the world.
Thus extension in length, breadth, and depth constitutes the nature of corporeal substance.
All of Descartes' physics rests on this one claim. The entire physical world, he is asserting here, can be explained as a function of extension. Every physical phenomenon, every observable event, can be accounted for just by logically reasoning about the principles of geometry—that is, the study of extended bodies. In this way, we can import the certainty of mathematics into the investigation of the natural world.
There is no real difference between space, or internal place, and the corporeal substance contained in it. The only difference lies in the way in which we are accustomed to conceive of them.
Since body is nothing but extension, Descartes claims that there is no difference between body and space. Bodies are not in space, as we normally believe; space is body. The only difference between space and the things we call bodies is that space has not sensible qualities such as color, hardness, smell etc. This is one of the central tenets of his physics.
Then motion is simply the transfer of one body from the vicinity of other bodies which are in immediate contact with it, and which are regarded as being at rest, to the vicinity of other bodies.
Like his explanation of space, Descartes' explanation of motion is a revision of the common conception. Motion is not an action separate from bodies themselves, but, rather, it is a property of bodies. Motion is a function of the position of a body relative to other bodies. It is, therefore, derivable from the principles of geometry, as Descartes thinks all physics must be.
Up until now I have described the earth and indeed the whole visible universe as if it were a machine: I have considered only the various shapes and movements of its parts. But our senses show us much else besides, namely: colors, smells, sounds, and such-like.
With this statement Descartes begins the last part of his treatise, the treatment of our sensations. There is nothing resembling our sensations out in the world, on Descartes' picture. In the mechanistic, mathematical model he presents, there are only the properties that can be logically derived from extension (such as shape and motion). Colors, odors, tastes, hungers, etc. are not derivable from extension, and so they do not exist in the physical world. However, these properties are a large part of our experience of the world (in fact, they are almost our entire experience of the world), and so he deigns in the last section of the last chapter to deal with them. Sensations, he tells us, arise as a result of the interaction of our physical organs with particles of matter, followed by the interaction of our physical organs with our mind. His theory of sensation is presented in much greater detail in a later work entitled, On Man.