There isn't really a precise, settled definition for "Occam's Razor". I'm going to — initially — set aside any qualification like "all things being equal" (because that's such a big escape-hatch that it doesn't leave much behind), and start with "The simplest explanation is usually the best one". Or, if you like, "We consider it a good principle to explain the phenomena by the simplest hypothesis possible" (which Wikipedia helpfully tells me is from Ptolemy).
With that out of the way, throughout history, theistic and supernatural explanations have been widely accepted as the simplest explanation for almost everything. The universe is complicated. Satisfying "naturalistic" explanations require a great deal of understanding, and for most of us (or, let's be honest, all of us), that understanding necessarily includes a lot of over-simplification and assumption.
That's why, over hundreds of thousands of years, countless theistic and supernatural systems have arisen, in every human society — and why those systems persist over hundreds and thousands of years. They are the simpler ones.
Explaining Something Simple
I have a rock, here, on my desk. A river stone: smooth, gray, oblong. It's nice.
What?
Consider the What of this rock.
From a scientific perspective, I know that it's probably basalt, and those sparkles mean there's some quartz in there.
I'm going to try to do this without resorting to Wikipedia. Let's see how it goes.
Hmmm, and, what... feldspar, I think, and some other things I don't remember.
Those are made up of elements of various sorts... silicon definitely, maybe calcium and sodium, and I think potassium. And there's oxygen in there, which is a bit weird because that's an important invisible part of the air around me. The oxygen makes fire, and I somehow need it to live... and anyway, there's some of that in the rock, but bound up in some way that won't cause fires and I definitely can't breathe it.
I know that this difference is because the elements are bound into molecules. I don't remember much about this, but I remember that different elements have different smaller particles. Neutrons, protons, electrons. There's a whole bit with electricity and charge there, but it doesn't matter right now, I don't think. The important thing is that the number of these different subatomic particles somehow (how? uh, honestly, no idea) causes the elements to behave differently. The protons and neutrons are stuck together by something called the strong nuclear force (which is, I'm told, fundamental), and the electrons stay in orbit (where they don't actually exist in any specific place, but kind of just as ... a probability cloud) around those due to a weak nuclear force. Or maybe the forces are the other way around. They're a basic fact of the universe, though, I know that.
Anyway, the electrons like to clump in energy-shells, which also like to be complete, and there's a pattern — I think 2 in the first one, and then 8 and the another 8 and I forget after that — and the electrons can be missing, or shared, and there's something about ions and anyway, this causes the different elements to bond into molecules, which can have completely different properties from their original elements. Or at least, mostly different. I'm unclear on how different, actually. The original element is important, I'm sure.
Anyway, these molecules: they're really little — like, so little that there's no way to make an optical device where I could see them. And, they're actually mostly empty space, between those particles, and also, they don't really touch each other, but somehow that makes a solid rock. Yes. Lots of different kinds of molecules, of different elements, with all those different properties, held together by various fundamental forces. That's a rock.
Or...
Stone is one of the basic building-blocks of the universe. You know, there's air and water and other water-like things, and wood and metal and stone. Maybe fire. Right here, what I've got is a nice example of stone. It's heavy. I mean, not as heavy as gold, but it's got a solid, satisfying heft. You can hit things with it, and it probably won't break, although if it does, it'll probably be a kind of sheer, jagged crack. Yep, that's rock.
How?
What about the How? That is, how did this rock come to be?
The science: well, okay, it's basalt. I think that's volcanic? But, not like obsidian or pumice. Something that got more melted than that, maybe? Anyway, there are other types of rock, like some that is squished bones and shells of tiny creatures. But I'm pretty sure this was formed millions or hundreds of millions of years ago deep inside the earth -- which is (mostly) solid on the outside, but has complicated molten layers in the inside, which are not solid but dense enough that we don't really worry about it too much, except when there are volcanos. This rock might have been some other rock a billion years ago, and then got melted down and mixed up and spit up, and then maybe was part of a mountain, and then some small part got chipped off and eventually ended up in a river and got tumbled around for thousands of years until it got all nice and smooth.
Oh, but before that! Those elements! Where did they come from? Wellll, the complicated ones, those didn't exist at the beginning of the universe. Wait, actually, at the beginning of the universe there wasn't any stuff. It was just all super-dense — like, everything was everywhere all at once, but there wasn't any "everywhere" for it to be in! But not a pinpoint, because that assumes that there's some "not everywhere" that this was in the middle of. No, this was all there was and there wasn't an outside of it. But for some reason (yet unknown) that exploded and there started to be space for there to be stuff in, and there was eventually hydrogen. I'm not sure why, but it all kind of came together that way.
So: hydrogen: the first element. Then, that element started clumping into stars, and so some of the hydrogen got squished so much it transformed into a totally different element — helium! I think we got some molecules around that time, too, but as far as I know whatever helium-hydrogen molecules exist don't factor into my life much. (Except that there was recently a Jeopardy! clue about what two elements were in the first molecule, so I feel like I'm on pretty solid knowledge-ground here. Like, rock-solid, if you will.)
I'll fast forward a bit, but: the first stars explode, more stars start making even heavier and more complex elements, eventually we get planets made out of those elements, and one of those planets is the Earth on which I live, and my rock was part of that, made out of star-stuff (just like everything else around me).
Also, I'm actually not sure that this isn't one of those kinds of rocks that's made up of a lot of little shells, really squished. If it is, there's probably carbon in it. And this inert thing was once hundreds or thousands of living beings. But I think it's the volcano kind of rock, which is definitely not made up of living things even though the elements are pretty similar, give or take the carbon.
Or
Wow, that was complicated. It's just a rock, expressing its general rock nature. The simplest explanation is that the universe has always been here, and that there have always been rocks. Maybe something made them. They're pretty great, rocks. Makes sense that someone would want to make them, if they had the power to do it. Same with trees. Good stuff.
Now then....
Don't get me wrong. I personally believe the complicated things about my rock. Even though I clearly don't really understand it. But it's so complex that this belief is really based on faith rather than experience. I do not mean this in some sort of wishy-washy "science is another religion!" sense. I think it's a well-justified faith: I believe that people have done careful, empirical research over centuries to test and verify all of that complexity. But, wow, it's complex.
Why?
So, let's consider the serious question: what's the purpose and meaning of this rock? Or: the Why.
Okay, so, finally, I can get simple with science! There is no why! The processes just happen, all of that stuff for billions of years, maybe some random chance bouncing things around, maybe some set pattern locked in at the beginning of time — maybe even something that repeats over and over. But it's just its own thing, with no external reason other than the explanation of what happened.
Turns out, people find this really hard to accept. I claimed that this is a simple answer, but in practice it opens up a lot of other questions. If the rock has no "why", does anything? How do we live without that? Is there any meaning to anything? Do our actions matter? This is not simple after all!
Or....
Ah, see, now this is easy. The main reason we have rock is so we don't fall through the earth. I mean, it could be something else solid — like, wood would work, but then, how would it get there? Or metal, but that seems like too much metal. So we've got rocks for that.
Maybe it's because the rocks like to do that. They feel good filling that purpose. I mean, not my rock. It's not holding anything up... it's kind of retired from that, and moved on to being an object of comfort and contemplation.
I can definitely see why, if there were some kind of creator beings, they would want to make rocks. Absolute basic stuff, in every sense.
It follows that there are equally satisfying answers to all those other questions about life, the universe, and everything. Nice! Tidy! Completely simple, really!
Is this convincing?
Maybe my "simple" explanations don't feel very simple. That's okay — there are probably a hundred other ones, too. I hope we can agree that the scientific-based ones are pretty complicated.
I am sure that we can agree that my terrible explanations are vast oversimplifications — really understanding the details of even a small part of any of that could be a lifetime's study, and still incomplete. And this is just about a rock.
So, back to what I left out at the beginning — "all things being equal", or other such careful caveats about "not requiring addition external explanations". I'm not at all convinced that it helps. What does it mean for things to be "equal"? It's so vague. And... every scientific answer definitely has another layer of complexity.
I'm back to Wikipedia for a second here, to bring up a strong form of the Razor, from Ernest Mach (as his "Principle of Economy"): "Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses."
Well, with everything being equal, here at my desk, the scientific approach went beyond "perceived by the senses" almost instantly. Even with elaborate equipment and a lot of time, most of that would actually be from inference and reason based on observation, not direct perception.
Of course, so do any explanations (mine or otherwise) that go to theological answers rather than simply observing the direct phenomena: but, all things being equal, those seem to be pinnacles of parsimony in comparison to the scientific explanations. (Consider this important moment from classic-era The Simpsons.)
So, what, then...
I think this answer to another question on the value of Occam's Razor overall really has something right. This is a useful rule of thumb with some subtle depth. But, it doesn't really provide any satisfaction when applied to the big questions. Maybe apparent-simplicity isn't a good metric for anything so important.