in my own words:-
The two most widely known of Descartes' philosophical ideas are those of a method of hyperbolic doubt, and the argument that, though he may doubt, he cannot doubt that he exists. The first of these comprises a key aspect of Descartes' philosophical method. As noted above, he refused to accept the authority of previous philosophers - but he also refused to accept the obviousness of his own senses. In the search for a foundation for philosophy, whatever could be doubted must be rejected. He resolves to trust only that which is clearly and distinctly seen to be beyond any doubt. In this manner, Descartes peels away the layers of beliefs and opinions that clouded his view of the truth. But, very little remains, only the simple fact of doubting itself, and the inescapable inference that something exists doubting, namely Descartes himself.
His next task is to reconstruct our knowledge piece by piece, such that at no stage is the possibility of doubt allowed to creep back in. In this manner, Descartes proves that he himself must have the basic characterisitc of thinking, and that this thinking thing (mind) is quite distinct from his body; the existence of a God; the existence and nature of the external world; and so on. What is important in this for Descartes is, first, that he is showing that knowledge is genuinely possible (and thus that sceptics must be mistaken), and, second, that, more particularly, a mathematically-based scientific knowledge of the material world is possible.