Bell's argument (1964; 1971; 1975) establishes a mathematical no-go theorem for theories of the micro-world. In its standard form, it derives that theories which are local (and full certain auxiliary assumptions) cannot have correlations of arbitrary strength between events which are space-like separated. An upper bound for the correlations is given by the famous Bell inequalities. Since certain experiments with entangled quantum objects have results which violate these inequalities (EPR/B correlations), it concludes that the quantum realm cannot be described by a local theory. Any correct theory of the quantum realm must involve some kind of non-locality, a `quantum non-locality'. In some sense, entangled quantum objects fundamentally depend on another, even when they are space-like separated.Widely accepted? No, the correct conclusion is that quantum mechanics does not allow a local hidden variable theory. Just read Bell's theorem on Wikipedia or any textbook. Of course the conventional wisdom since 1930 has been that no hidden variable theory of any kind is possible.
While this general result is widely accepted, there is a large debate about what kind of non-locality exactly follows from the violation of Bell inequalities.
People who should know better say crazy things on this subject.
Cornell solid-state physicist David Mermin has described the various appraisals of the importance of Bell's theorem within the physics community as ranging from "indifference" to "wild extravagance". Lawrence Berkeley particle physicist Henry Stapp declared: “Bell’s theorem is the most profound discovery of science.”.If you think that Bell proved nonlocality, then you would consider it very profound. But if you realize that Bell only rejected some theories that everyone rejected anyway, then it is no big deal. That is why there has never been a Nobel Prize for work related to Bell's theorem.