Noncognitivism is a position on religious language and religious words like "God" which says that they have no cognitive content -- i.e., that they are meaningless. Noncognitivism says that the word "God" is a placeholder that isn't holding a place for anything in particular; that because "God" is supposed to be "metaphysical," it refers to nothing, tells us nothing, and means nothing. Thus the phrase "God exists" can't be true or false.
Religious believers use the term "God" all of the time as if it were obvious that something coherent and meaningful were meant by it. Although theists act like they mean something by the word, when pressed to explain themselves it often turns out that they don't mean anything in particular because they can't explain in clear, coherent terms just what they think they mean.
A.J. Ayer & Logical Positivism
The concept of noncognitivism and using the apparent meaninglessness of so much religious language against religion can be traced back to A.J. Ayer, who argued that statements like "God exists" can't even be considered true or false because there is simply no empirical way to evaluate them.[I]f "god" is a metaphysical term, then it cannot be even probable that a god exists. For to say that "God exists" is to make a metaphysical utterance which cannot be either true or false. And by the same criterion, no sentence which purports to describe the nature of a transcendent god can possess any literal significance.
- A.J. Ayer, Language, Truth, and Logic. (1936)
A.J. Ayer's noncognitivism is a logical outgrowth of his philosophy of Logical Positivism. Developed by Morris Schlick, Rudolf Carnap, and other members of the Vienna Circle, Logical Positivism was introduced to the English-speaking world by A. J. Ayer in his Logic, Truth, and Language, from which the above quote is derived. Here is a more complete version to provide context:
What is not so generally recognised is that there can be no way of proving that the existence of a god, such as the God of Christianity, is even probable. Yet this also is easily shown. For if the existence of such a god were probable, then the proposition that he existed would be an empirical hypothesis. And in that case it would be possible to deduce from it, and other empirical hypotheses, certain experiential propositions which were not deducible from those other hypotheses alone. But in fact this is not possible.
It is sometimes claimed, indeed, that the existence of a certain sort of regularity in nature constitutes sufficient evidence for the existence of a god. But if the sentence "God exists" entails to more than that certain types of phenomena occur in certain sequences, then to assert the existence of a god will be simply equivalent to asserting that there is the requisite regularity in nature; and no religious man would admit that this was all he intended to assert in asserting the existence of a god. He would say that in talking about God, he was talking about a transcendent being who might be known through certain empirical manifestations, but certainly could not be defined in terms of those manifestations.
But in that case the term "god" is a metaphysical term. And if "god" is a metaphysical term, then it cannot be even probable that a god exists. For to say that "God exists" is to make a metaphysical utterance which cannot be either true or false. And by the same criterion, no sentence which purports to describe the nature of a transcendent god can possess any literal significance.
Verifiability & Meaning
A focal point of logical positivism, alluded to in the above, is the verifiability criterion of meaning. Ayer argues that the sentence "God exists" cannot mean anything unless it is at least theoretically possible to support or falsify it through empirical observation. If "God exists" is an empirical hypothesis about the world, then it must be possible to deduce from this certain likely observations that we might seek out. If no such deductions are possible, then there is no way for us to come up with evidence for or against the claim -- and that means that it isn't a meaningful, empirical statement.
The importance of this was developed further by Antony Flew in his book Reason and Responsibility (1968):
Let us begin with a parable. It is a parable developed from a tale told by John Wisdom in his haunting and revolutionary article "Gods." Once upon a time two explorers came upon a clearing in the jungle. In the clearing were growing many flowers and many weeds. One explorer says, "Some gardener must tend this plot." The other disagrees, "There is no gardener." So they pitch their tents and set a watch. No gardener is ever seen.
"But perhaps he is an invisible gardener." So they set up a barbed-wire fence. They electrify it. They patrol with bloodhounds. (For they remember how H. G. Well's The Invisible Man could be both smelt and touched though he could not be seen.) But no shrieks ever suggest that some intruder has received a shock. No movements of the wire ever betray an invisible climber. The bloodhounds never give cry.
Yet still the Believer is not convinced. "But there is a gardener, invisible, intangible, insensible, to electric shocks, a gardener who has no scent and makes no sound, a gardener who comes secretly to look after the garden which he loves."
At last the Sceptic despairs, "But what remains of your original assertion? Just how does what you call an invisible, intangible, eternally elusive gardener differ from an imaginary gardener or even from no gardener at all?"
The parallels between Believer's alleged gardener and theists' alleged God should be obvious. Believer has constructed a claim about a gardener which, it seems, is no different from an imaginary or nonexistent gardener.
In order for Believer's claim to be different (and to be taken seriously as meaningful), it would be necessary for there to be some observable state of affairs which make the existence of the gardener more likely than not or some observable state of affairs which would make the existence of the gardener less likely. In other words, there must be some observation which would tend to support or falsify the claim. In the case of Believer, no such observation appears possible.
The same is typically true of what theists claim as well. Very often there doesn't seem to be any difference between a world in which they say "God exists" or "God loves us" and a hypothetical world in which it would be true to say "God does not exist" or "God does not love us." Theists need to be able to differentiate between the two in order for their claims to be empirically meaningful. Otherwise, why should anyone really care about what they are saying?

