Digital Zoom is simply cropping an image (taking the center portion of it out, then discarding the remainder, to make it look like more optical zoom was used).
It then takes this smaller center portion of the image, and enlarges it using interpolation, back up to the original image resolution.
This interpolation process adds pixels to the image to enlarge it, based on the values of adjacent pixels. However, interpolation can only add pixels, and does not increase the detail that was present.
So, quality degrades rapidly, as more Digital Zoom is used, since you only have as much detail as was present in the crop of the image (actual number of pixels captured by the camera to represent your subject).
You can accomplish the same thing later with software - -with more accuracy for the crop, using better interpolation techniques than you'll find in the camera.
I keep Digital Zoom disabled on my camera.