Agnosticism in its original sense (i.e., as coined by Thomas Henry Huxley in the 1840s), is the belief that it is impossible (perhaps in principle impossible) to know for sure whether or not God (in some sense of 'God', but typically the God of monotheistic religions) exists. It can also be applied to the belief that there is evenly-weighted evidence on both sides of the question of whether God exists. The word comes from the Greek a (no) and gnosis (knowledge). Among the most famous agnostics (in the original sense) were Huxley, Charles Darwin, and Bertrand Russell. Russell's Why I Am Not a Christian is a classic text of agnosticism. It can be and has been argued that David Hume was an agnostic; one might infer that from his Dialogues Concerning Natural Religion, but this is a widely-debated question, and no one really knows for sure what religious views Hume held.
The term has come to be applied, by some, to the simple failure to hold that God does or does not exist (i.e., not taking a stand). In this sense, the twentieth century logical positivists, such as Rudolph Carnap and A. J. Ayer--who believed that talk of God and perforce considerations of whether one can know that God exists are simply nonsense--would count as agnostics. The freethinking tradition of atheism calls "agnosticism," used in this sense, negative atheism.