The physics department just had a talk by a researcher from Wilfred Laurier University, discussing the EPR (Einstein-Podolsky-Rosen) Paradox. This is a very counter-intuitive quantum effect which is very difficult to describe. The speaker this afternoon did an excellent job of describing it in regular language. I was very impressed. It really is true, you can only really explain something to someone else once you fully understand it yourself.
In short, Einstein, Podolsky and Rosen were bothered by the weirder conclusion from quantum mechanics. So they proposed an experiment that you could do which would show that the quantum model was incomplete. Unfortunately for them, the counter-intuitive results of the experiment actually did occur, proving that quantum mechanics actually is correct. This experiment was the beginning of quantum entanglement, and all of the wonderful weirdness which grew out of that.