Stem cell research is accosted (to put it mildly) for being unnatural; relationships between certain groups of people are derided as unnatural; arbitrary miscellaneous things are condemned for not being natural; hair colouring products are advertised as looking natural and being made from natural ingredients. But what the bloody hell is “natural” supposed to mean anyway?
You could argue that anything that isn't caused by a human is “natural”. While this is clear, it's not very useful: it's just assigning blame to a particular species rather than telling you anything fundamental about the questionably-natural thing.
There's a well-known and prestigious science journal called Nature, whose title goes straight to the crux of what science is about: describing nature. So you could argue that anything that can be described by science is thereby natural. This seems fairly reasonable at first glance.
However: two hundred years ago, Brownian motion wasn't understood at all; one hundred years ago, radioactivity wasn't understood at all either. Further back, lightning and comets were sources of wonder—no-one knew what they were or how they came to pass. No-one has ever (seriously) suggested that these were anything but natural phenomena.
And science is constantly progressing—ever more phenomena are being understood each year. But this doesn't mean that those phenomena were previously supernatural or unnatural and have now, by virtue of our understanding of them, suddenly become natural.
There's that tricky “our” again: who are “we”? All humans? Humans plus some hypothetical human-like aliens? If these aliens' science understood a phenomenon that humans didn't, would it be natural? If so, such a phenomenon would be natural, but without humans (or even a second species of hypothetical human-like alien) knowing that it was; naturalness would then become a seemingly random property of which one could never be sure—not very useful. If aliens don't count, we're back to defining naturalness on the basis of an arbitrary species (those pesky humans again).
Are they natural? They're certainly not human-made, but I doubt many would assert that they were a natural phenomenon. That designation is reserved for things more like the weather: complex (or even simple, actually) systems of inanimate matter producing an interesting or noteworthy result (this is how we'll describe a “phenomenon”) by processes governed by The Laws Of Nature™. That's science again.
But psychology is a science too. (Yes, it is.) Human behaviour is arguably governed, and if so it's by rules that psychology describes.
(By the way, The Laws Of Nature™ are also just a description, rather than a prescription—things don't happen the way they do because The Laws™ say so; rather, The Laws™ say what they do because that matches how things actually happen. That's a surprisingly common misconception among non-scientists.)
So we have “natural sciences”: typically physics, chemistry and biology. Things like astronomy, palæontology, geology and ecology come under that banner as well, though ecology does stray towards being heavily human- and animal-influenced. And then there are “human sciences”: about half of geography, economics, sociology and arguably history, for example.
But psychology doesn't fit clearly (as far as I'm concerned, anyway). It's definitely about humans and animals, but it's also intricately linked to biology.
Zoology is usually considered a natural science as well, because it's not about humans, though it is about animals. But is it about nature?
I think the usual assumption of “natural” being “anything that we (humans) haven't touched” comes back to human arrogance and self-centredness. (For millennia we humans thought our planet was at the centre of the universe because, why, we're here.)
I'd suggest that a process is certainly “natural” if it involves nothing that can think. (Of course, there's then the problem of how to determine what's alive and conscious and can think.)
Clearly, though, the existence of beings that can think is natural. And it seems somewhat masochistic to say that because one is capable of thinking about whether what you're doing is “natural” (which is assumedly virtuous) that it therefore isn't natural.
So, I don't know. I have a clear idea of what sort of things are and aren't natural, but I have no idea what definition of “natural” the apparently-obvious distinction arises from.
Just one more thing: being unnatural is certainly not necessarily a bad thing: buildings are unnatural but very useful. For the environmentally sensitive, solar power cells are unnatural but useful. Also: clean water from a tap; electricity; eyeglasses; most medicine.