The extension has common files (jquery etc) requested included with it, and list of CDN curls that return those files. Every time browser makes request to those urls, the extension serves the local file back.
How does that help? It speeds up browsing, since you have local version of the requested file. It also increases privacy. For example many sites are lazy and use for example google cdn for let say jQuery. Now when you visit the site, google still can track you, because you make request to them.
The only weakness with this approach is that it only works for urls known to the author. Request to unknown CDN or even known CAN, but a new file will still be made (AFAIR there is an option to block unknown files on known CDN, but that will often break many websites)