remoteStorage.js is a client-side library to add remoteStorage support to your client-side app. There is a tutorial for example usage and more info in the readme of the repository.
Basically, remoteStorage is an open standard to decouple web apps from per-user data storage – whereas at the moment, most web apps are an app+storage package deal. Check the website of the unhosted movement for more info, and feel free to join our chat room if you have questions.
Since the RSS reader is fully client-side and hostable on Github, it would be very fitting to use remoteStorage to allow people to save their feeds.