Even though this isn't exactly accurate, the way I like to think of Descartes' hyperbolic doubt as stating that there's no way to prove that information gained through sensory experience is accurate. After all, in a dream, the dreamer fully believes that his experiences are 'real', but they are not, which he only discovers in retrospect.
I wonder, however, how deeply this is tied to a much less popular (today, that is) belief of Descartes, that the functions of the mind are mainly the products of an immaterial soul which relates to the body but is independent of it. If the mind is materialistic, and even Descartes believed that his own mind must exist ('mind' being defined as merely a consciously thinking thing) then does it necessarily follow that that the mind receives chemical signals from a body, which have sense organs stimulated by an external world, etc. and thus get out of Cartesian (or hyperbolic) doubt?
I've also heard that Descartes' doubt could be solved by appealing to evolution: in order to survive, wouldn't the mind need to correctly perceive its surroundings?
(Please see my own answer before posting a different one)