This is the sort of thing that gives me goosebumps. How do they do it? Well, a few parts of the brain are like topogaphic maps. The most famous one is probably the somatosensory cortex, where it is possible to draw a homunculus across it. It is a little out of proportion, of course, since not all areas receive equal amounts of sensory input, but that doesn't matter. The principle still holds, namely that this portion of brain is spacially mapped in a predictable way to the design of your body. In plain English, this means that you can pick a point on the somatosensory cortex that represents the knee, and if you know which way is 'up' in the brain (to the right, in this image), you can easily predict that the chest area must correspond to a bit slightly to the 'right' of the knee on the brain.
I hope I haven't lost you already! Anyway, a part of the primary visual cortex is also mapped predictably according to which retinal cells are activated. If you know how the two correspond, and if you possess an accurate enough way of visualising the visual cortex (which is right at the back of the head), then you can convert your information about which cells in the visual cortex are firing back into the original image. And that's exactly what these researchers have done, to the limits of present day technology.
Anyway, there's a wonderfully clear write up on the issue over at Pharyngula here. Enjoy!