The secret to this idea of focusing and re-focusing an image after it's been shot is in the way it's shot. I'd try to explain in my own words, but I think the website does a better job of it:
Recording light fields requires an innovative, entirely new kind of sensor called a light field sensor. The light field sensor captures the color, intensity and vector direction of the rays of light. This directional information is completely lost with traditional camera sensors, which simply add up all the light rays and record them as a single amount of light.So, with all of this data stored in this image file, you can adjust the focus -- quite dramatically -- after you've taken the shot. Both the blog for this product and the how-to videos talk about staging a photo or looking for a specific type of shot to take to get the most out of this camera... it's not the sort of thing that works well when you take a picture of two people standing next to each other against a wall, for example. You need to establish the various depths-of-field in the shot in order to really see it work.