Descartes' justification of the mechanistic world-view was made on the basis of his claim that one could achieve certainty only with judgments made on clear and distinct concepts provided by the mind itself, rather than sensory experience. Enlightenment philosophers spoke of these concepts which the mind alleged provided as provided by "Reason" or as "innate" to the "faculty of Reason." Hence Descartes and all philosophers who hold the view that such innate concepts are the foundation of knowledge are called "rationalists," and this epistemological view is called "rationalism."
While all rationalists agree that "Reason" provies the foundation for knowledge, they all differ amongst themselves with respect to which concepts they hold Reason provides. In Descartes' case, the particular form of rationalism which he defended led him to claim we had knowledge of two different kinds of beings or entities, those he called "res cogitans" or "substances the essence of which is to think" (proved in the famous cogito argument of Meditation II) and "res extensa" or "substances the essence of which is to be extended" (i.e. to be in space and time). For short, we call these two kinds of substances "minds" (res cogitans) and "bodies" (res extensa).
Thus Descartes' rationalist epistemological theory lead him to hold a particular metaphysical theory (theory about the nature of reality), namely that there are two kinds of beings or, as he called them, "substances." Because it aserts there are two kinds of beings, such a theory is called "dualism," in this case it is often identified with Descartes by calling it "Cartesian dualism" or "mind/body dualism."
According to such a view extended substances or "bodies" are fully described by mechanistic physics. As such they are substances having only the primary properties of extension, those which are necessary to characterize them as moving through space over time in terms of mathematical concepts. All other proeprties not essential to mechanical description are regarded as "secondary," and are held to be reducible to the action of bodies possessing only primary properties acting on human sense organs. As such the secondary proeprties are not really "there" in the body, but exist only in our sensory perception of the body.
The other half of Descartes' dualism are substances having the properties of thinking things, or "minds." These substances (by 'substance' Descartes means 'that which has properties') have the properties of having ideas, making judgments, and acts of willing. They are not in space and time, and therefore not described by the mathematical laws of mechanistic physics. Our knowledge of what minds are comes not from a mathematical description but from a direct awareness of our own conscisouness, as Descartes concluded in Meditation II.
This metaphjysical view has nice virtues, particularly with respect to Descartes attempt to forge a compromise between the claims of religion and science. But it also has a looming difficulty. Human beings are 'somehow' a combination of the two; we are both a mind and a body, but how do two substances which "have nothing in common" (Descartes' own description of them) relate to each other? It certainly seems as though things that happen to my body produce ideas in my mind and ideas in my mind cause movements of my body, but how can this be explained on Descartes' view? His own answer was to say they "interact" (hence his view is called "interactionism"), but that's only a way of papering over our ignorance with an empty word. If it really is the case that they "have nothing in common" how can they interact? This problem is called the "mind-body problem."
Many attempts to solve the mind body problem have been proposed, but none has been succesful. Today most philosophers would say that the problem as Descartes set it up is insoluble, and therefore the only way to overcome it is not to get into it in the first place. Since the problem arises because of Descartes' acceptance of dualism, we can get out of it if we reject this conclusion and assert only one half of Descartes dualism is ultimately or "independently" real. Any view which does this is therefore "monistic."
Obviously, there are two ways to go: we could eliminate the mind half or we could eliminate the body half.
If we eliminate the independent reality of minds, we assert only bodies are independently real beings. When we talk about "minds" or other "mental" properties like ideas, beliefs, acts of will, etc., we are really just talking about special ways of behaving of bodies, in particular of bodies called "human brains and central nervous systems." For philosophers who take this path, ultimately everything said about "minds" and mental properties will be "reduced" to a purely physical description of bodies; minds are not "independently" real. Another name for the substance which is supposed to possess the properties of extension (i.e. whose essence is to be in space and time) is "matter" or "material substance"; so this view is called metaphysical "materialism." Much twentieth century philosophy is materialistic in this metaphysical sense. [Do not confuse this use with other uses of the word "materialistic."]
The other path taken by different philosophers is to reject the view that material substances are independently real. According to this view only minds are independently real substances. When we talk about "bodies" (and the whole physical world of space and time) we are refering to what are really properties of minds, specifically those properties known as sensory perceptions. Bodies are indeed the things we perceive, the things we see, feel, etc., but they exist only a perceptions in thinking minds. Thus bodies are not "independently" real. This view is known as metaphysical "idealism." Much nineteenth century philosophy was idealistic in this metaphysical sense. [Do not confuse this use with other non-metaphysical uses of the word "idealism."]
A great deal of philosophy from the time of Descartes to our own day is concerned with battles between dualists, materialists, and idealists. Indeed these debates are often seen as the very heart of philosophy in the "modern" period (i.e. philosophy since the Enlightenment).