Non-local, in layman's terms, means things in vastly different places being able to affect each other instantaneously. The implication is that it is impossible for one particle to very quickly affect the other by sending a virtual particle (or even message), as this would mean the particle travelling faster than the speed of light (and that would be 'a bad thing'!).

So instead of breaking c, we assume things with non-locality that particles 'spookily know'/are affected by things that may possibly be on the other side of the universe. This causes a myriad of problems in the actual physical interpretations.

I remember thinking as well, hey why don't we just accept non-locality, but, actually doing physics with it you end run into myriad headscratchers that even make the broken Copenhagen look attractive! One that I did for my MSc was for the case of an single electron in a (harmonic was it?) potential well and solving for a stationary state. By dealing with the Bohmian waveguide model you end up getting that electron is experiencing no overall force - therefore it is literally stationary (serious problems there!) or moving at a constant speed, and could be ANYWHERE in space (non-locality). So your could have 'bound electrons' that are over in Mars or... aren't moving? I'll put up a work through of that if anyone wants to check! Just one example, but my professor (a very thoughtful guy) thought it was cute, had its uses in some applications, but sadly probably not the right story.

I already knew what non-local was, but the examples of no force hence stationary and completely non-local is indeed what I was interested in.

Would love to see that worked through in more detail!