I'm guessing that it works similarly to low-budget astrophotography but with the computer doing all the busywork for you: when you want to photograph stars or planets and you don't have a fancy tracking mount to compensate for earth's rotation you'll have very mediocre results with long exposure. If you expose a lot to see the object clearly then you get motion blur. If you use a shorter exposition to reduce the blur you don't have enough light to get a clear picture.
One solution is to take a bunch of low-exposure pictures in a row and then add them together (as in, sum the value of the non-gamma-corrected pixels) in post while taking care of moving or rotating each picture to line everything up. This way you simulate a long-exposure while at the same correcting for the displacement.
An other advantage is that you can effectively do "HDR": suppose that you're taking a panorama with the milky way in the sky and some city underneath it, with a long exposure the lights of the city would saturate completely. With shorter exposures you can correct that in post by scaling the intensity of the lights in the city as you add pixels (or summing fewer pictures for these areas). This way you can effectively have several levels of exposures in the same shot and you can tweak all that in post. In the case of the city/milky way example you'll also need to compensate for the motion in the sky but obviously not on land which is also something you can't really do "live".
I have a strong suspicion that it's basically what this software is doing: take a bunch of pictures, do edge/object detection to realign everything (probably also using the phone's IMU data), fit the result on some sort of gamma curve to figure out the correct exposition then add color correction based on a model of the sensor's performance under low light (since I'm sure by default under these conditions the sensor will start breaking down and favor some colors over others). Then maybe go through a subtle edge-enhancing filter to sharpen things a bit more and remove any leftover blurriness.
If I'm right then it's definitely a lot of very clever software but it's not like it's really "making up" anything.
