What are nonlocal hidden variables?
Solution 1
Bell's theorem says the following. Suppose that each measurable quantity for a system is described by a stochastic variable  a single number picked out of a hat. The stochastic variable's value might depend in some way on other values you don't know about or can't measure  hidden variables. In order to match the predictions of quantum mechanics, the variables of spatially separated systems would have to influence one another nonlocally  without any signal passing between them.
So Bell's theorem means that any other theory that reproduces the predictions of quantum mechanics either works by some means other than hidden variables or it is nonlocal. A nonlocal hidden variable theory would just say that there are hidden variables but they are nonlocal. Such a theory wouldn't get around Bell's inequality  it would claim that the inequality is correct and says that the laws of physics are nonlocal.
I would also say it seems strange to talk about getting past Bell's inequality. The inequality is either right or wrong. You should be clear about either accepting it or refuting it  getting past is a vague description that leaves your position unclear.
There are other responses to Bell's inequality that don't involve accepting that the world is nonlocal, such as trying to explain the outcomes of the relevant experiments by applying quantum mechanics instead of trying to find another theory that reproduces its predictions. Quantum mechanics doesn't have hidden variables  rather each system is described in terms of observables represented by Hermitian operators:
https://arxiv.org/abs/quantph/9906007
Solution 2
If you know what are local hidden variables, then any variables outside that is nonlocal variable.
Local variables (hidden or otherwise) is the information/plan stored inside the entangled particles at the time they depart. Whether hidden or not is a different question. I think they are called hidden because they would be stored in the entangled particles and not visible to outside observers.
Any other mechanism/plan/influence would be nonlocal.
Not necessarily true, but an example can be  Suppose the measurement of previous pairs somehow are remembered by the environment and that memory influences outcome of measurement of subsequent pairs in such a way that quantum predictions are matched. By environment, I mean one or more of  creation equipment, measuring equipment, space in the vicinity of the experiment.
This would be considered a nonlocal influence because it is not stored inside entangled particle at the time of creation. It would rather accumulate in the environment as we measure more and more entangled pairs and the accumulation would steer the overall outcome towards quantum predictions. This kind of influence does not need to act at FTL. Simple sub luminal speeds would be sufficient in such a mechanism as it has plenty of time to act over duration of experiment.
This phenomena is named as memory loophole. There can be other possibilities which can be given some other name. All nonlocal possibilities are called loopholes by QM community.
Allmost all entanglement experiments geared towards proving two things 
 Bell's inequality is violated
 All loopholes (nonlocal influences) are closed.
Any data sets that do not prove these two things, are discarded as erroneous data.
I am ready for the down votes:)
Related videos on Youtube
A. C. A. C.
Updated on July 14, 2021Comments

A. C. A. C. about 1 year
It is said that Bell's Inequality basically denies all possible local hidden variables theories as solutions to entanglement but what does a nonlocal hidden variable theory mean and how does it get around Bell's Inequality?

Admin over 3 yearsI think it would be worth pointing out the consequences of nonlocal hidden variables ever becoming nonhidden: causality violation. So because hidden variable theories must be nonlocal by Bell's theorem, such hidden variables must (assuming we don't want causality violation) not be observable even in principle. That's a bit like the aether or something: this thing in the theory which can never be detected, and that makes many people pretty uncomfortable with such theories I think (certainly me).

user21820 over 1 year@tfb: That's actually not right. We cannot observe nonlocal hidden variables in full, but that by no means implies that we cannot observe them at all. It's not conceptually any different from a wavefunction, which we can never measure in full but can measure approximately at a chosen point.

CommaToast about 1 yearNonlocal hidden variables could work like global variables in computers, where a single location in memory gets referred to from multiple different local scopes that don't share local variables. The existence of nonlocal hidden variables could weakly support the idea that the universe is a simulation.

alanf about 1 year@CommaToast philosophy.stackexchange.com/questions/56796/…

CommaToast about 1 year@alanf I'm not convinced by Deutsch's arguments or your summary of them. The Halting problem and Incompleteness Theorem are limits on the ability to make statements about things, however they don't block you from creating a full simulation because youtu.be/xP5iIeKXE8 the Game of Life can run in the Game of Life without having to know if a given pattern ever halts. A simulation can be a full simulation without needing to be able to predict what will happen next in inside itself.

CommaToast about 1 year@alanf Deutsch tried to torture Cantor's proof of the uncountability of the real numbers to make a claim about simulations but it's complete nonsense. I mean he completely hamfisted it. He says, "Suppose all possible environments produced by this generator can be laid out sequentially" but then his argument is that a finite generator is finite so therefore it's not "real VR" or some bullshit. Well what if the computer running the sim, itself grows in its own reality, as the simulated reality grows? Deutsch is an idiot (sorry).

CommaToast about 1 yearHe says, "Suppose all possible environments produced by this generator can be laid out sequentially" but then he mentions "altering" these states, creating new states that are not in the sequence (which contradicts the first statement that says "all possible environments produced by this generator can be laid out sequentially". It's bogus AF.

alanf about 1 year@CommaToast Your comments misstate Deutsch's position, so the arguments you present are irrelevant. For example, Deutsch claims that any physical system can be simulated by a universal computer, so your claim that he denies the idea that it would be possible to make a full simulation is false.

alanf about 1 yearThere are other problems with what you write. For example, the point of supposing that there is a list of all possible environments and then showing there is an environment that isn't on the list is to show that supposing the existence of the list leads to a contradiction so no such list can exist. This kind of argument is called proof by contradiction: to understand it better see "Proof and the Art of Mathematics" by Joel David Hamkins, especially Chapters 1 and 13.

CommaToast about 1 yearI know that it's a contradiction but it doesn't prove anything. It does not support the point he was trying to make.

CommaToast about 1 yearAlso I am not convinced that "any physical system" can be simulated on a classical computer. A Universal Turing machine has no way to simulate quantum randomness. The best it can do is to use a pseudorandom algorithm. It could use an external source of randomness, but if it does, then it's not really simulating randomness. Also, I'm skeptical a classical computer could simulate quantum nonlocal effects; I would be warmer to the idea of a simulation of our reality being possible on a quantum computer or hybrid.