Quantum mechanics was a tool developed to talk about things that aren't known. It can be completly rewritten in terms of probability theory because Quantum theory doesn't assume it knows about things it doesn't know anything about. For instance, if you keep your eyes closed, and open them briefly, and see a cat to your left, and then a short time later, you open them briefly and see a cat to your right, you might assume the cat has moved from left to right. Quantum mechanics, at its root, does not make these assumptions. It says that while your eyes are closed, there are an infinite set of possible occurrences that can get the cat from one moment to the next. The cat might be picked up and moved by something else, or teleport magically, or sneak about behind you, etc. etc. From your perspective, you can't know anything about it, so you have to talk about what happened in the most vague and cryptic terms imaginable. If you took all that talk, and expressed it mathematically, you'd be talking about the wavefunction.
As it turns out, if you look at that mathematical expression, which is the sum of all the unknown possibilities and all the unknown probabilities, you can use it, play with it. One person might look at the equation and say, "there is no cat, only the observation of a cat.". Another person might say "the cat is a wave, being to my left at one time and to my right at another time and everywhere else instantaneously at all other times". Another person might say "There's a cat, and it walks from left to right today". Others say "There are infinite cats, and you observed two of them". All are perfectly good interpretations of what is going on while you get some shuteye, but that doesn't mean they have a clue, they just sound smart.
What's important about that is that I can use the mathematical representation of that system and do mathematical experiments on it, and test a given hypothesis. If I flash a flamethrower between the space left and right while my eyes are closed, and the cat isn't on flames on the right when I open them, I've learned something about the system, but I've also done a new form of observation, namely, that the cat is on fire. I've changed the system. I can do the same experiment in a cat-friendly way, with mathematics, and observe how I can't observe without causing change. But, I can also design better experiments than flamethrowers and cats by using the mathematic tools.
What's more, is that the equations, while unknowable and unsolvable, have a set of properties and laws, and seem to look like the math of probability and the math of waves. I can apply approximate solutions in a strict and proper way, and test to see if my approximate solutions hold up to real observation. Since they behave like waves, I can also use an infinite sum of waves in the same dimensional space to reexpress the system, and assume some of the harder to solve waves are small and neglectable. I can also see if the functions predict any strange behavior, and look for that strange behavior. For instance, quantum mechanics says if I approach a wall that is penetrable but not within my personal power to do so, there's a finite (albeit small) probability I'll wind up on the other side. While there's a few people who have claimed to see me do that, there are a much larger group of scientists who have observed electrons do that, because you can generally get a large group of electrons together giving it a go much more easily than you can find people like me. The power of quantum mechanics is not idle talk about what talk about quantum mechanics is. It's about giving up the need to know why, and assuming anything's possible, and working from there.
That may sound like the last (and coincidentally most popular) choice [The unmeasured world is literally made up of vague (not determined) possibilities.], but it's not. The point is that there is no mathematical difference, in the quantum mechanical model, between infinite universes, infinite vague possibilities, and a real universe made up of real things appearing just the way they are. If there is any lesson in quantum mechanics, it is that such talk is at its root idle bullshitting, and until one can devise a good experiment to prove that infinite universes exist, or whatever, keeping one's mouth shut on the subject is prudent. Unless, you can find a way to make a quick buck off of it, or found a religion about it. David Bohm, for instance, was quick to do the latter.
It's about not talking about what you think you know, but instead talking about what you observe, what you can observe.