Non-overlapping magisteria (or NOMA) is the name given by Stephen Jay Gould to his beliefs regarding the compatibility of science and religion. It is outlined in an essay of this name[1], and expanded in Rock of Ages.
Gould states that the province of science is the empirical universe: questions of how things are, and why those things are so. Religion, then, has its realm "questions of moral meaning and value". He then notes that there are many things which are not in either - listing art and beauty as examples. Gould contends that if rigidly adhered to, the NOMA principle ensures that science and religion do not conflict.
Critics of NOMA point out that religion does make claims that fall into the scientific arena, and that it is hard to imagine a religion that does not, and so NOMA is unworkable. It may be so that if religion were to provide maximum benefit to society, it would be best if it stayed out of the realm of science, and science would serve society better if it did not try and provide answers to normative ethical problems for which it is not qualified. It would seem that most religions do not plan to become Gouldian any time soon. Richard Dawkins also argues in his response to Gould that he sees no reason why religion has any monopoly on moral meaning and value as Gould claims[2].