Bell's theorem turns a conceptual question about quantum correlations into an experimentally testable inequality.

A local hidden-variable model assumes that measurement outcomes are determined by additional shared variables while a choice made at one location cannot instantaneously influence the outcome rule at a spacelike-separated location.

For suitable pairs of binary measurements, these assumptions constrain the correlations. In the CHSH form,

$$|S|\le2.$$

Quantum mechanics predicts entangled states and measurement settings for which

$$|S|>2,$$

up to the quantum bound $2\sqrt2$.

What a violation establishes

Experimental violation of a Bell inequality rules out the class of local hidden-variable explanations satisfying the assumptions used to derive that inequality. It is stronger than merely observing that two distant results are correlated.

What it does not establish

Bell violations do not allow faster-than-light signalling, because each local measurement record remains compatible with the same local random statistics until results are later compared.

They also do not, by themselves, select one unique philosophical interpretation of quantum mechanics. Different interpretations account for the same experimentally observed Bell correlations in different ways.

Bell's result therefore gives a precise boundary on classical-style local explanations without turning an experimental inequality into a broader claim than it supports.