Erwin Schrödinger proposed this thought experiment without any intent that it be taken seriously. He certainly never actually put a cat in a box with a vial of deadly poison. He intended it as a damning counter-argument to the Copenhagen Interpretation of Quantum Mechanics.
In short, the math of QM tells us that there's no reason for a particle to exist in one state rather than another. The Many Worlds model (popular with authors of speculative fiction, for reasons that are probably obvious) states that the particle exists only in one state in this universe, but in other states in other universes, leading to a branching infinity of possible universes. As an untestable hypothesis, this isn't popular with scientists, particularly since other models are testable and have been confirmed to be true.
The Copenhagen Interpretation states instead that if a particle can exist in multiple states, that it does exist in multiple states. Imagine walking into the kitchen and, rather than choosing to sit in one particular chair, you instead sat in all of them at once. Perhaps 80% of you is in chair A, while the remaining 20% is spread evenly across chairs B-F. In QM math terms, that's saying that the wave function1 tells us there's an 80% probability of finding you in chair A, 4% in B, 4% in C, 4% in D, 4% in E, and 4% in F. If we looked 100 times, roughly four of those would find you in chair C. More than that, though, the Copenhagen Interpretation tells us that until we looked you wouldn't just be in one of those chairs, you would actually be in all of them simultaneously, but more in A than in the rest.
Therefore, Schrödinger argued, according to the Copenhagen Interpretation, the wave system of the cat in the box is 50% undecayed isotope/alive cat, 50% decayed isotope/dead cat. Conclusion: The cat is simultaneously alive and dead. This is stupid2. This is a reductio ad absurdum, taking an argument to a logical and absurd conclusion to demonstrate that the argument is false.
And it's hard to argue with. It proceeds ineluctably from the mathematics of QM to the well-tested and confirmed knowledge we all share about the way death works to demonstrate that the Copenhagen Interpretation is false. And Schrödinger was a really smart guy whose name is still all over QM and he must have understood it, right?
Then why is the Copenhagen Interpretation the number one interpretation of physicists today? Why is it the one taught in schools as the truth while others get, at best, a passing mention? Mostly because it accords with all the evidence, and also because Schrödinger made a little mistake. Actually, a big mistake.
First, the evidence. If a system can exist in multiple configurations simultaneously, then it doesn't merely bounce from one to the next to the next. It actually does exist in all of them simultaneously. Every measurement we can do on electrons and molecular bonds, and extended metallic or ionic structures confirms this. A chemical bond that's half a single bond and half a double bond actually is somewhere between the two, not one or the other at different times.
Second, Schrödinger's mistake. It's rather similar to the one made by Roger Barrier in an article I discussed elsewhere. It's the mistake of not knowing exactly what an observer is. Douglas Adams, brilliant and trenchant as always, noted in Dirk Gently's Holistic Detective Agency that the cat itself counts as an observer! However, he got it wrong as well.
The Geiger counter is the observer. It's the one that measures whether or not the isotope has decayed and actually makes the "decision" to release the poison. In the same way, when you read these words on your screen, you yourself are not the observer that collapses the wave function. The single molecule in your eye that captures the photon is itself the observer, not you. The Geiger counter captures the energetic particle released by the radioactive decay and transforms that energy into an audible click. The molecule in your eye captures the photon, is transformed into a high energy state that then, through an awesome, high-fidelity QM process transfers that energy downhill and into your brain where... something happens so your brain can process it. I don't actually know much neurology. Brain is pink thinky thing. It's a goop.
Anyway, the point is that the cat is not simultaneously alive and dead. By continually observing the isotope, the Geiger counter is keeping the isotope's wave function collapsed in the "undecayed" state until such time as it hopes over into the "decayed" state and the poison is released. And the moon is being continuously observed, but God doesn't have to do that, because everything in the universe that interacts with the moon, from the Earth, to the sun, to every single particle in your body, is doing that whether you notice it or not. When a tree falls in a forest, everything around it observes that fact. It does make a sound. Reality exists absent our perception of it.
Just try to remember, there's a reason "scientific" "proofs" for the existence of a god aren't being shouted from the rooftops and taught in schools. It's because they're wrong. That's why I put them in quotes up there. There are a few scientists, a minority, who are both fully educated in their field and who also believe in a god of some kind, but they almost all, with only a few, eye-roll-inducing exceptions3, stay far, far away from any statement of the sort "Scientific Theory X proves that my god exists."
1 - A wave function details all the information about a system, whether it's a particle in a box, the electron around a hydrogen nucleus, or the 92 electrons around a uranium nucleus.
2 - Yes. It is. Don't argue. This is the world of the everyday we're talking about. You're alive or you're dead. Even if you're in a persistent vegetative state and your brain is dead but your body is still alive, then your brain is dead and your body is alive but it's still not fifty fifty.
3 - Like the doctor who recently made the news for saying the afterlife was real. He made Newsweek. And it was terrible science.