Most Linux distributions offer mirrors that use rsync.
I know that rsync is best used on mirrors because it only copies the delta between the local file and the remote one.
What benefits do I get as a user from using a rsync mirror?
In the case of Archlinux, rsync is used to keep mirrors in sync with each other. This allows them to contact each other, and only transfer packages that have been updated or newly created. The package installer (pacman in Arch's case) on individual machines however uses HTTP to fetch new packages. rsync could be used for this last step, but it's features aren't needed, and HTTP is more likely to be able to go through firewalls (or through proxies, if required). I believe most other distributions use a similiar setup, with several tiers of mirrors kept in sync with rsync, and the final step from mirror to the package installer using either HTTP or FTP.
There really isn't any reason why you would use a rsync mirror directly, unless you are trying to create your own second-tier mirror.
The first time you use it, none.
Subsequent times, you receive deltas (i.e. updated changes) only, therefore you experience significant bandwidth and time savings.
Some other reasons to use rsync would be...
A "mirror" probably refers to mirroring a Linux distro/repo? (a linux distribution?) ... but if you have no use for that local copy of a Linux distro/repo (mirror) then there is no reason to do it. Many organizations mirror (keep a local copy) of a Linux distro so they have faster access to it. Basically it's just caching. (keeping a fast local copy).
I use rsync to backup my data... to update a second copy of my data so that in a bad situation I have a backup (second copy) of my data that's up to date. I do backups every hour, and it takes less than a second. (my data doesn't change that fast).
That's all rsync is for... keeping a second (or subsequent copy) up to date.
Or maybe you meant why would you use a mirror of a Linux distro rather than the primary copy? That's really only to lower the load on the server with the primary copy and the network between you... if there is a closer/faster copy of the same data then why wouldn't you use it ...as long as you trust that it is an accurate and up to date copy. Don't use a mirror if you have doubts about it.