Basically, the light field lets you reconstruct a series of images of your subject as seen from every patch of your lens. Of course, for subjects not at infinity, this means multi-view images. This enables
(a) 3D reconstruction, by multi-view matching and having precisely known geometry.
(b) segmentation, by using 3D reconstruction as mentioned above.
(c) Super-resolution, again by multi-view matching, which can let you get back some of the resolution you lost by capturing the image as a "light field" (which means that your sensor can tell which direction the rays hitting it come from - it's done by having an array of lenses in front of the sensor, each covering a patch).
Better segmentation of the image enables all sorts of higher computer vision algorithms.
Whether this technology is any good as a consumer photography product, I am not the one who can say.