What does the Dream Hypothesis allow Descartes to doubt?

The dream hypothesis as articulated by Descartes was a method by which he sought to doubt the existence of the world around him (the 'external world'), on the grounds that he might be dreaming. (What if I'm really dreaming, and this fire here is only a dream of fire, and this table here is also a dream etc...)

From this he concluded that the only thing of which he could be certain was that he existed, inasmuch as certainty presupposed someone's being certain ("I think, therefore I am").

Descartes' methodology of doubt was analyzed by many philosophers afterwards, most penetratingly Kierkegaard.

What probably constitutes the most profound refutation of Descartes would be Wittgenstein's later thoughts, stemming from GE Moore's initial commonsense analysis of the dream argument.