It’s when you want to focus on something in particular, with the rest being out of focus, caused by depth of field. Ik shamelesly stole a picture from @Twozzok in the photography thread to illustrate this:
See how the plant in the foreground is in focus but the background isn’t. Depth of field isn’t a common feature in point & shoots, I know some of the high-end current ones can do it, but apart from that.. My Canon point & shoot can’t in any case, except in macro mode. So the above picture isn’t achievable for the snapshot photographers.
I’ve been following this tech on Engadget, the concept is great, the technology promising, but this product isn't a serious photography tool. It’s a great (and expensive) toy, in my eyes. It’s great for Facebook pics and the like, they don't require a high resolution. This thing does its uses, it’s too bad image quality doesn’t seem to be to great (although to be honest, I haven’t seen any real user experiences and examples yet). But you have to realise, this thing is fast. If you want to capture things “in the moment”, this is great, you can make a snapshot in 3 seconds or so, and you can adjust focus afterwards to suit your needs. It would be very different with a real camera, where you at least have to check what the camera is focussing on, before you can take a picture. This camera removes all the need to “think” about your picture. That said, I think it’s too expensive at this point, for some sort of point & shoot.. If you don’t mind taking a bit more effort in taking pictures, I hear the Sony Cybershot DSC-HX9] (for example) is a great point & shoot, which is cheaper, and does a lot more with greater image quality.
If I had the money to spare, I’d buy this thing just for the gadget factor (I love the form factor by the way, no it’s not ergonomic, but since it’s small it can get away with that).
Also, it’ll be a while before this will be implemented in other (“more serious”) cameras. It requires a whole different sensor, and the sensor in this thing is quite big. I don’t know how fast they’ll make it small enough to be used in conventional cameras, whether point & shoots, milc’s or dslr’s. And then there’s still the matter of the known camera manufacturers willingness to license this stuff, unless they want to develop their own lightfield sensors.
Edit: Had a look again at the site, it’s not the sensor which is big, but rather the image processor.