Good question, but I'm sure they'd like to keep the 'how it works' a secret, at least, beyond what they say on the site and in press briefings. Here's my conjecture, I may be completely wrong, I am only guessing how it might be done applying technology to give the described functionality, since the cynic in me doesn't believe hype and doubts the items for sale really are as different as they would encourage us to believe.
The images in the gallery appear to consist of no more than an image map overlaid on several discrete photos of the same scene, which one you view (shot at a different focus distance) depends where on the image you click your mouse. I could manually make something that does that on a webpage in html4, let alone html5 with a handful of images of the same scene. Sure, it would take me a while to construct, but it is do-able.
So, the clever bits are:
a) they have camera that 'instantly' captures (my guess) 9 x 1.3 MP images of a scene, each focused at a different focal distance by overlaying a standard 12 MP sensor with a 3 x 3 grid of miniature lenses with different focal distances.
b) they store that image and at some point before it becomes viewable they;
b1) superimpose the 9 images onto 9 layers
b2) do some adjustments of perspective to correct parallax issues between them for the objects nearest to the camera, as they would otherwise show slight movement
b3) run a pseudo auto-focus detector over the 9 image layers and map which bits are sharpest on which layer
b4) add a new top, tenth layer which holds the results of the mapping, so when you click on the area of an image that has something close, it displays only the image layer that bit was sharpest on
I had a play in their picture gallery and yes, while it's all very clever, I can't see it being any advance for a serious photographer of the like that frequents CiC.
Think about the compromises (I haven't played with a camera, so this is guesswork too);
you probably lose the ability to choose an aperture and hence control of Depth of Field,
the image viewer (just one at a time) controls focus, what do they know about what we wanted to be the point of focus (and DoF)?
you can't change the lens, you're stuck with their 8x one (focal length range unknown to me as I type, but I bet it is biassed toward wider angles),
it is probably auto exposure, so no control of shutter speed either.
How would you print it? (One layer, or the best of all to get DoF back?)
Sharpness at infinity is very unimpressive.
I have yet to see any image that is larger than a megapixel in content.
Notice also; a lack of any images with significant movement close to the camera in it?
It is a bit like 3D TV, works best at close range.
It is no more than a glorified P&S, by dint of image processing, it avoids the need for an iris (always wide open, hence no flash needed for indoor shots), no serious controls (touch screen access only)
Might be ok for party night use and FB, allowing people to focus on themselves.
If I suddenly disappear, you'll know I was right and they 'got me'
After getting that off my chest I do actually think, given my position, I should say "The views above are my own and do not represent those of Cambridge in Colour", just in case 'they' go 'legal' instead of 'lethal'