Naturalism is hard to define, since it can mean anything from a substantive metaphysical worldview (i.e. Ontric Structural Realism) to a body of scientific methods. Philosophers tend to make a distinction between metaphysical naturalism and methodological naturalism. The former is a monistic position that only Nature exists, whereas the supernatural entities do not exist. The latter is more or less about the scientific methods we use to understand the natural world without presupposing supernatural entities. Many philosophers call themselves naturalists, but what a “naturalist” means can vary among individuals. My naturalistic worldview is more or less inspired and informed by Spinoza, who was often called a pantheist by his critics. Spinoza, however, tells his friend in a correspondence that: “as to the view of certain people that I identify God with Nature (taken as a kind of mass or corporeal matter), they are quite mistaken.” Spinoza does not believe God to be a corporeally composite universe, but rather an “eternal substance” or unified principle that encapsulates the very nature of existence. The physical universe is just an ephemeral manifestation of an underlying process.
I don’t entirely agree with Spinoza’s metaphysics, but I think the spirit of his metaphysics is on the right track. What I think Spinoza got right is that the reality we live in is a coherent self-sufficient reality. What this means is that all parts are arranged together in a unified whole ( called “Nature”) according to its own fundamental laws and structure (this is neutral between whether or not such laws or humean or non-humean). Nature is coherent insofar as every part is interconnected with each other as a multifaceted nexus and self-sufficient insofar as it acts only from its own structure and laws. Consequently, nothing in Nature transcends it, since it encompasses everything. Whatever exists must exist in Nature. In effect it is explained in a relevant context of Nature. What this also means is that we do not need a transcendental explanation at all. Some (especially theists) might ask how Nature came into existence. I won’t give a substantive and well argued answer to that question in this entry, but I do lean to an idea that some things are brute facts. Nature’s fundamental structure may just be a brute fact that necessitates explanations, but prior to itself there is no causal explanation. This means that unlike Spinoza I’m not necessarily committed to the principle of sufficient reason. This doesn’t mean that the universe does not have a beginning. It probably does, but that doesn’t show that it has a cause in a way that individual existing entities have cause. Nature just might be a self-contained system that does not require an explanation from beyond.
This is just my very sketchy conceptual scheme of Naturalism. I’m still not sure how mathematical sets, moral facts, consciousness, intentionality, and such can fit into this scheme, but I can only assume that they must (for now).