Intuitive

• A particularly nice interactive explanation can be found here, and also here.
• The best explanation for Bell's theorem in layman terms, can be found in The Quantum Theory and Reality by d'Espagnat
• Another nice explanation can be found in this reddit comment.
• Another creative explanation in laymen terms can be found in The mystery of the quantum cakes by P. G. Kwiat and L. Hardy

Concrete

• A simple proof of Bell's inequality by Lorenzo Maccone
• http://mateusaraujo.info/2016/07/15/understanding-bells-theorem-part-1-the-simple-version/
• Bell's Theorem with Easy Math by David R. Schneider
• See also David Mermin's paper, "Bringing home the atomic world: Quantum mysteries for anybody" Am. J. Phys. 49:940-943(10), Oct. 1981, free PDF.
• Daniel M. Greenberger, Michael A. Horne, Abner Shimony, Anton Zeilinger "Bell's theorem without inequalities", American Journal of Physics Vol. 58 (12), December 1990
• For another nice discussion, see What could not be in Feynman lectures: Bell inequalities by V. Cerny

Abstract

• A nice overview is given in this Nature article.
• A modern reformulation of Bell's theorem is No extension of quantum theory can have improved predictive power by Roger Colbeck & Renato Renner (Nature)

Why is it interesting?

Bell’s theorem is the most profound discovery of science. Henry P. Stapp, "Bell's Theorem and World Process", Nuovo Cimento, Vol. 29B, No. 2, p. 270 (1975).

Bell's theorem says that reality must be non-local. Nick Herbert Quantum Reality - Beyond The New Physics Chapter 12, Bell's Interconnectedness Theorem, p. 212

History

• John Bell and the most profound discovery of science by Andrew Whitaker

Criticism

• Bell’s theorem is wrong at Project Tartarus

Jaynes vs. Bell

"The measurement at A at time t does not change the real physical situation at B; but it changes our state of knowledge about that situation, and therefore it changes the predictions we are able to make about B at some time t 0 . Since this is a matter of logic rather than physical causation, there is no action at a distance and no di culty with relativity [also, it does not matter whether t 0 is before, equal to, or after t".Clearing up the Mysteries, by Jaynes

A critical discussion of Jayne's point of view can be found here.