It's been said that when you get the message, hang up the phone. What is "the message" though? I can't dictate what it is for everybody. This was just my biggest "aha moment" in recent years.
The most commonly expressed version of this idea I have seen, by analogy, is that living beings are like the countless little eyes which make up a compound eye. Each seeing a narrow, limited perspective of the world. The "big picture" which only the overall eye can see is all of those combined.
You could also express it as similar to the way in which a picture on a monitor is made up of many little differently colored pixels. There doesn't appear to be any rhyme or reason to it until you zoom out far enough.
In the same way, a human being viewed up close is actually trillions(!) of tiny individual organisms, none of which know they are part of a much larger creature. All expressions of the same basic idea that we're all part of the same thing, connected in ways that are not immediately obvious until viewed on a grand scale, and that separation is to some extent an illusion.
I experienced the same apparent self-evident nature of this idea but my brain is wired such that it is unsatisfied with that sort of just-so answer. I want complete explanations, diagrams with every little part clearly labeled. I want to know how it works. So I kept chugging away at it until this occurred to me:
In biological evolution, simple chemical self-replicators gave rise to intelligent organisms such as ourselves. We know this to be true with quite a lot of certainty.
Humans will eventually develop self-replicating machines. This is a plausible assumption given present technological trends toward automation, and probably occurs on any planet where intelligent life evolves. (Providing they don't destroy themselves first)
Since self-replicating machines will reproduce the conditions that started biological evolution (simple replicators), we have reason to believe the same thing will happen - resulting in the evolution of machine intelligence (Even if we do not make them intelligent to begin with).
These machine intelligences will assume dominion over their environment (which at their technological level will likely be anything reachable by spaceflight) just as humans, the previously evolved intelligent beings, asserted dominion over the earth. This is a reasonable expectation based on extrapolation of forces we have observed to produce this outcome already.
Self-replicating machine intelligence, wherever and however it originates, will set about converting all accessible matter in the universe into computational substrate, as that is the equivalent of habitable living space for intelligent machines (as opposed to, say, a Dyson sphere or O'Neill cylinder).
Finally, once the entire universe is converted into a single vast thinking machine, the universe may link to other universes (the few which arrived at the same outcome due to having similar laws to our own) to form a network of neuron analogs, forming the neural network some consider the supreme being.
Even though individual universes eventually run out of energy (heat death), this does not kill the larger organism described here for the same reason that individual cells in your brain can die and be replaced by new ones over time without interrupting your continuous experience of consciousness.
If you subtract labels like "robot", "biological", "technological" and so on from it, what's described there is just a tendency for the matter supplied by the big bang to undergo a process driven by the energy it also supplied, gradually self-organizing into intelligence (like humans, most recently).
Note that essentially the same outcome occurs no matter what. For example, if self replicating machines or strong AI are impossible, then instead the matter of the universe is converted into space colonies with biological creatures like us inside, closely networked. "Self replicating intelligent matter" in some form, be it biology, machines or something we haven't seen yet. Many paths, but to the same destination.
Humans die out? No problem, plenty of other intelligent life has already arisen before and will arise after us, like how it's no big deal if any given sperm fails to reach the egg since there's plenty more where that came from. And so on and so forth. It will seem highly speculative until you exhaustively try to find a way for it not to turn out as described. Then you will discover that all roads lead to Rome, as it were.
Note also that nothing described here is supernatural. Just matter and energy obeying the laws of physics. This concept does not contradict any of what science has so far revealed, but instead relies upon and extrapolates from it. It is in fact descended from the same lines of evidence and reasoning which commonly lead people to atheism, just thought through further than usual.
I don't consider this knowledge necessary. It's entirely possible to live a fulfilled life without it. I chopped wood and carried water before and still do. But I appreciate it because at the time I was feeling lost, and anxious about the future, worried that perhaps it was all up to humanity to spread life/intelligence (of some kind, be it biology or machinery) into space and perhaps we'd fail, destroying ourselves before we could accomplish that or whatever. Now I realize that while that's what we're here to do, it's not the end of the world if we fail.
There's a lot more to it; this concept intersects very neatly with the probabilistic argument for simulationism and a bunch of other related concepts. Incidentally I believe this to be the same thing Terrence McKenna dubbed the "transcendental object at the end of time" and which John C. Lilly named the "solid state intelligence". But that's a topic for another article. I figure it's enough to present the basic core concept to you fine fellows for the time being.
BBC: What if the Aliens We're Looking For are AI?
Popular Mechanics: Why Superintelligent Machines Are Probably the Dominant Lifeforms in the Universe
CBS: If Aliens Arrive, Expect Robots
Universe Today: Is Our Universe Ruled by Artificial Intelligence?
Nautil.us: Why Alien Life Will Be Robotic