This is pretty sweet. What optimizations does it do other than offloading stuff to CDN?
But offloading things to CDN is actually one of the things it doesn't do. You might be thinking of the PageSpeed Service [1] which is a Google-hosted version.
Note that docs above are for mod_pagespeed (Apache), but all of the same filters are available in nginx port as well - it's the same C++ code under the hood. In a nutshell: HTML, CSS, JS, and image optimization (resizing, recompression, WebP, auto-spriting, etc...)
Configuring ngx_pagespeed: https://github.com/pagespeed/ngx_pagespeed#how-to-use