The SH has beeen expressed through various thought experiments, but none so famous as Descartes' Evil Genius from the end of the first chapter of the Meditations on First Philosophy. There Descartes imagines a being of infinite power and knowledge who is equally malevolent and who entertains herself by deceiving us. How could we know anything if such a being used all her powers against us.
A more contemporary version of the SH is the Brain-in-a-vat hypothesis: suppose aliens remove your brain and place it in a vat of nutrients and attach it to a computer which feeds it stimuli which exactly imitates sensory data. Could you, under such circumstances, know that you are reading this entry on your computer? After all, you're just a brain in a vat which is being caused to think you are reading this on your computer.
The strength of the SH is that the skeptic need not believe it to be true. The point is not to prove our beliefs are false, but merely show that they could be false; this is sufficient reason to embrace some degree of skepticism.