It appears to be a two-step process; first, you figure out the blur kernel, then you use that kernel to unblur the image. The white line in the blur kernel represents the path of the camera while the shutter was open, and consequently it's a map of how a single pixel gets "smeared" to create the blur.

The second step seems fairly straightforward. Standard blur features like gaussian blur use a kernel to spread the value of a single pixel to its neighbors (that's called "convolution.") With a known kernel, a similar convolution could get the original image back.

The magic here is the first step -- creating the blur kernel directly from an already-blurred image.