This article doesn't quite aim to be an intuitive explanation of quantum mechanics. What it does is, however, closely related, and may be of interest to anyone who wants to know more about quantum mechanics: it's a simple explanation of Bell's inequality and it's experimental violation. It's the violation of Bell's inequality which essentially forces us to abandon our ordinary realist conception of the Universe. This is perhaps the strongest single piece of evidence in favour of the quantum mechanical view of the Universe.
(Disclaimer: I wrote the article.)