It relates to the idea that science is limited by its insistence on adhering to methodological naturalism. According to this view, science cannot investigate the supernatural. The view is popular among some who oppose creationism since it means that creationism can't be scientific, by fiat. It's also important for accommodationists because it allows science and religion to co-exist in separate magisteria.
I oppose such a definition of science but, up until a few years ago, I was always told that my opinion is irrelevant since all philosophers, and many scientists, agree that science is limited by methodological naturalism. That's why I was so delighted to meet the philosophers from Gent. Finally there was another point of view opposed to the methodological naturalism limitation. Now those who promote this limitation on science have to honestly admit that it's just their opinion and not a universally accepted definition of science.1
Good News from Gent
Methodological Naturalism - How Not to Attack Intelligent Design Creationism
Here Be Dragons
An Interview with Maarten Boudry
Here's the abstract of the Science & Education paper.
According to a widespread philosophical opinion, science is strictly limited to investigating natural causes and putting forth natural explanations. Lacking the tools to evaluate supernatural claims, science must remain studiously neutral on questions of metaphysics. This (self-imposed) stricture, which goes under the name of ‘methodological naturalism’, allows science to be divorced from metaphysical naturalism or atheism, which many people tend to associate with it. However, ruling the supernatural out of science by fiat is not only philosophically untenable, it actually provides grist to the mill of anti-evolutionism. The philosophical flaws in this conception of methodological naturalism have been gratefully exploited by advocates of intelligent design creationism to bolster their false accusations of naturalistic bias and dogmatism on the part of modern science. We argue that it promotes a misleading view of the scientific endeavor and is at odds with the foremost arguments for evolution by natural selection. Reconciling science and religion on the basis of such methodological strictures is therefore misguided.And here's a brief summary of their position ...
A widespread philosophical opinion conceives of methodological naturalism as an intrinsic and self-imposed limitation of science, as part and parcel of the scientific enterprise by definition. According to this view (Intrinsic Methodological Naturalism or IMN) – which is the official position of both the National Center for Science Education and the National Academy of Sciences and has been adopted in the ruling of Judge John E. Jones III in the Kitzmiller vs. Dover case – science is simply not equipped to deal with the supernatural and hence has no authority on the issue.3The distinction between Intrinsic Methodological naturalism (IMN) and Pragmatic Methodological Naturalism (PMN) is important. PMN is a conclusion based on centuries of scientific evidence strongly suggesting that natural explanations are sufficient to explain all phenomena. Those investigations include looking onto possible supernatural explanations.
In our view, however, methodological naturalism is a provisory and empirically anchored commitment to naturalistic causes and explanations, which is in principle revocable in light of extraordinary evidence (Provisory or Pragmatic Methodological Naturalism – PMN). Methodological naturalism thus conceived derives its rationale from the impressive dividends of naturalistic explanations and the consistent failure of supernatural explanations throughout the history of science.4
Scientists have actually investigated possible miracles and found no evidence for them. Scientist have actually investigated the supernatural explanation for a world-wide deluge and refuted it. And if someone says that God made bacterial flagella, real scientists will try and find out whether that's true instead of just throwing up their hands and claiming that such an explanation is outside of science.
The implications of PMN are profound. It means that science and religion really are in conflict.
1. Of course the accommodationists will admit no such thing as I'm sure you are about to see in the comments. Such an admission would require them to say that they mislead Judge Jones in the Dover trial.