I have to think David will agree, on reflection, that his answer has failed to capture the essence of entanglement. Any stream of particles, if not specially prepared, will measure +h/2 or -h/2 at detector A; they will do with respect to the x axis, or the y axis, or any axis. Exactly the same is true at detector B. How can this very ordinary circumstance illustrate the mystery of entanglement? But that seems to be what David has said: that if you prepare the particles in the entangled state, you get this "strange result". I see nothing strange about it since it seems to be exactly the same result if you set up two detectors far apart and measured streams of particles that were totally random.
I am going to suggest that the mystery of entanglement lies in the perfect correlation (or anti-correlation) that you get when you set up both detectors along the x axis. Some people think there is nothing mysterious about this because it is exactly what you would expect if the two particles were created with equal and opposite spins. These people are very wrong. The reason they are wrong is that the experiment works the same no matter how you align the detectors with respect to the source of the particles. We can imagine an experiment where particles are created with opposite spins, but assuming the spin axis is random at the moment of creation, there is no way a pair of detectors should show 100% correlation no matter what angle you set it to. In fact, in the case of entanglement, there is 100% correlation regardless of the orientation. That is a real problem and it is really the only problem.
EDIT: I explain this issue in more detail in my blog article, "Entanglement and the Crossed Polarizers".