Naturalism is any of several philosophical stances, typically those descended from materialism and pragmatism, that reject the validity of explanations or theories making use of entities inaccessible to natural science.
As described by W. V. Quine, who is in large measure responsible for naturalism's current pre-eminence among American philosophers, it is the position that there is no higher tribunal for truth than natural science itself. There is no better method than the scientific method for judging the claims of science, and there is neither any need nor any place for a "first philosophy," such as (abstract) metaphysics or epistemology, that could stand behind and justify science or the scientific method. Therefore philosophy should feel free to make use of the findings of scientists in its own pursuit, while also feeling free to offer criticism when those claims are ungrounded, confused, or inconsistent: philosophy becomes "continuous with" science. (Naturalism, that is, is not a dogmatic belief that science is entirely correct; it is the position that science is the best explanation we have. We have to start somewhere in talking about the world, and we don't have better evidence for anything other than science; yet as we go along we can still change it as we use it.)
There is currently some dispute over whether naturalism rules out certain areas of philosophy altogether, such as semantics, ethics, aesthetics, or excludes the use of mentalistic vocabulary ("believes," "thinks,") in philosophy of mind. Quine avoided most of these topics, but some recent thinkers have argued that even though mentalistic descriptions and value judgements cannot be systematically translated into physicalistic decriptions, they also do not need to presuppose the existence of anything other than physical phenomena. Donald Davidson, for example, has argued that individual mental states can (must, in fact) be identical with individual brain states, even though a given kind of mental state (belief in Santa Claus) might not be systematically identified with a given kind of brain state (a particular pattern of neural firings): the former weakly "supervenes upon the latter. The implication is that naturalism can leave non-physical vocabulary intact where the use of that vocabulary can be explained naturalistically; McDowell has dubbed this level of discourse "second nature."