Descartes is most famous today for two developments - Cartesian coordinates, which still play a key role in mathematics, and dualism, a philosophy which proposes a sharp distinction between body and soul, matter and spirit. According to Cartesian dualism, the spirit is personal and nebulous, and matter must therefore be impersonal and concrete.
In Descartes's image of the universe, matter is immersed in an unseen, immeasurable medium called the ether. God endowed the universe with movement at the beginning of time and allows it to run spontaneously but in accordance with his will. Because in this scheme matter fills all of space, there can be no such phenomenon as a vacuum and all motion is produced by matter impressing on other matter within the medium of the ether. Descartes expressed this in his famous theory of vortices, in which he pictured movement, such as the fall of a stone to the earth, as being like the movement of a feather or a straw caught in an eddy or a whirlpool.
Descartes rejected mysticism and the occult in his writings and visualised the universe as a machine. Every action involving matter was purely mechanistic, and matter had no contact with spirit. To Descartes, all animals - including humans - were also mere machines. Humans had a spiritual aspect, a soul, but this had no link with our Physical selves.
These ideas were highly controversial. On a scientific level, Descartes's concepts were unverifiable and he did not contrive experiments to support his theories. On a superficial level, his vortex theory did not clash with the doctrines of Galileo, in that it did not contradict experimental evidence. Galileo had shown that, because of inertia, all movement continued until stopped, and Descartes proposed that the universe had been set in motion by God. The two ideas were not incompatible: if we assume the Creator set things in motion they would continue until stopped by,  say, the intervention of mortals.
But the most radical aspect of Cartesian philosophy was that it implied to many that, once the universe had been set in motion, God was no longer needed. The Creator had been effectively demoted from 'Supreme Good' to 'First Cause'. Naturally this was a view hotly disputed by theologians and the majority of philosophers, many of whom had been brought up on Aristotle and still thought along the same lines.