The program is designed to take a reference file (presumably your original video source) and then compare it to any number of derivatives (e.g., a series of reencoded clips that were produced using different settings) to produce objective quality comparisons, outputted in either peak signal-to-noise ratio (PSNR) or structural similarity (SSIM).
This tool is perfect for individuals who like to tinker with encoder settings to find exactly what works for them. Now, instead of hunting through activity logs searching for quality measures, you can batch-encode a series of clips with your settings, then run them all through qpsnr and see what effect each setting had on quality.
It is only available as a source download at the moment, but the author suggested deb binaries will be posted after more testing is done. If not, I'll package some up in my PPA repository.