Short answers, pulled from the story.
Bell's theorem, derived by John Stewart Bell in 1964, shows that any classical theory based on local hidden variables must satisfy a mathematical inequality, but quantum mechanics predicts a violation of that inequality. This gave physicists a way to experimentally test whether nature obeys local realism or the stranger rules of quantum mechanics. The first experiment confirming the violation was conducted in 1972.
John Stewart Bell was born in Belfast, Northern Ireland on the 28th of July 1928. He graduated from Belfast Technical High School at 16, then earned two bachelor's degrees at the Queen's University of Belfast in 1948 and 1949, and a PhD in physics from the University of Birmingham in 1956.
Bell showed that von Neumann's proof against hidden-variable theories relied on a physical assumption that is not valid in quantum mechanics, namely that the probability-weighted average of a sum of observables must equal the sum of their individual averages. He reportedly called the proof "not merely false but foolish." The same flaw had been identified earlier by Grete Hermann in 1935 but had not become widely known.
Bell did not win a Nobel Prize. He died on the 1st of October 1990, and reportedly had been nominated for the prize that same year without knowing it. The Nobel Prize in Physics was awarded in 2022 to Alain Aspect, John Clauser, and Anton Zeilinger for work on Bell inequalities and the experimental validation of his theorem.
Bell coined "beables" to describe the elements of a physical theory that correspond to things that actually exist in reality, independent of any observation. He contrasted beables with observables, arguing that a truly precise physical theory should not depend on undefined concepts like measurement or apparatus. He favoured Bohm's hidden-variable theory partly because it offered this kind of observer-free description.
The John Stewart Bell Prize was created in 2008 by the Centre for Quantum Information and Quantum Control at the University of Toronto. It is awarded every other year for significant contributions published in the preceding six years. The first award was presented in 2009 by Alain Aspect to Nicolas Gisin for his work on quantum nonlocality, quantum cryptography, and quantum teleportation.