To give context to this question, I am currently looking into non-locality / hidden variables / Bell's Theorem, EPR / etc.
I've noticed the assertion that the values / state of something when measured aren't what the values / state would be if the measurement were not made.
How is this known? Or is it an assumption?
I have no science background so please explain in layman's terms, if possible.
At the risk of confusing you even more: the value "that would be if the measurement was not made" simply does not exist. Take a your favourite simple quantum system, e.g., the spins of two electrons. The values of the various components and combinations of their spin do not exist before you decide which observables you will measure. It is simply impossible to assign coherent (=non-contextual) values to all possible measurements that could choose to make, that don't depend on your choice what you will measure.
You may want to read about the Kochen-Specker theorem, it shows that choosing what you measure does not just "change existing values" of your observables, but "brings them into existence".
See, e.g.,
