Naturalism can be defined in many different ways, but a useful one is that it represents the idea that things happen because of natural causes and not for any particular purpose.
A naturalistic explanation about life on earth, for example, is that it is the product of natural causes, i.e., chemical molecules attaining the ability to replicate, and then evolving by modification and selection. And, of course, this explanation is true.
Acceptance of naturalism does not, however, imply atheism, as some prominent atheists seem to believe. The argument seems to be that if things are perfectly explained by natural causes, then there is no room for god: the assumption of the existence of god, is not necessary.
A commonly used argument against this explanation is that of natural exceptionalism. This argument goes like this: the world can be explained naturalistically, but the deity can bend the rules and suspend their operation, operating miraculously.
This argument is not very persuasive, since it requires that one should document the existence of miracles, and miracles are notoriously difficult to document to a skeptic's satisfaction, and rightly so.
However, miracles (*) are not necessary to support a theist's belief in god.
We can think of a digital computer whose operation is perfectly predictable: its state at any point in time is precisely determined from its state at previous points in time. The computer's operation can be precisely determined by the digital logic of its circuits, the oscillation of its clock, and the contents of its memory. It is thus a perfectly naturalistic system, whose operation is precisely determined by natural causes.
Nonetheless, computers typically compute "something". At short time scales, a scientist examining the computer would be able to discover some natural "laws" governing its operation, say, that when a particular instruction is read from memory, the content of two memory locations is added and placed in a third one. A whole repertoire of such laws could be determined, and the scientist could predict the computer's operation exactly. Nonetheless, this would give him no knowledge about what the computer was actually doing, what the purpose of the computation was.
The naturalist is content with determining the "laws of nature". But, the laws of nature are simply the allowed moves in the "game of reality", they are the instruction set of the universe. Knowing them tells us nothing about whether or not the unravelling computation has a final cause or not, whether it aims to compute something or not.
From this perspective, the atheist resembles a chess spectator who is able, by observation, to determine the rules of chess, e.g., that bishops move diagonally and rooks along straight lines, but claims that the game has no inherent purpose. The theist on the other hand believes that the sequence of legal moves are not meaningless, but rather aim towards a goal, which is victory. (**)
It seems to me that the theist has a much better ground to stand on than the atheist. Even though we are unable to determine the goal of the universe's evolution (if any), we can still observe it, and draw some tentative conclusions.
There are 2n n-bit long programs, for example, yet only a tiny fraction of them compute anything meaningful. You could fill up your computer's memory with random junk, and it would still work by following the random instructions. Our observation of the universe looks nothing like a random program however; it looks more like an orderly and well-behaved program, so, in my opinion, the idea that it has a purpose is more defensible than the idea that it does not.(***)
(*) It should be noted that the idea of a miracle as a suspension of natural law is modern, dating to the post-Newtonian period and the worldview of the world-as-a-clock. In the original sense, miracles (Gk. θαύματα) are extra-ordinary phenomena that cause a sense of wonder (θαυμάζειν) and are not "supernatural" events, but rather rare events, outliers.
(**) Chess is actually a great example of this, since the game itself is finite and can be computed. Of course, the number of possible chess games is finite, although very large, but in principle, a superfast computer could determine whether an optimally played chess of game will lead to a white victory or a draw, even though we have no idea what the answer will be. But, our inability (as humans) to compute the answer to "chess" does not mean that it does not have a clear (albeit exceedingly difficult) solution.
(***) Atheists often use an anthropic argument against this observation; they claim that all possible sets of laws are operating, and we are lucky enough to be in a region where the laws tend to allow for intelligence. This argument is not very persuasive though, since it postulates an infinite number of non-observable realities. Moreover, intelligence could very well have evolved in a tiny patch of order of an otherwise chaotic universe; it would not make one iota of difference for life on earth if, e.g., gravity operated differently in galaxies billions of light years away. The fact that not only our small patch of reality that is the solar system, but the entire observable universe is orderly is a pretty good argument against anthropic explanations.