How do I make use of the remote disc icon in the sidebar of Finder?
Remote Disc is a way for Macs without optical drives (Air, mini) to access another computers optical drive over a network. So you can put a disc in another Mac or Windows PC and read it on your mini.

Full details and instructions are reported here.

On the computer with the CD/DVD drive: 


Go to the Preference panel, and click on "Sharing."


In Sharing, enable the "CD and DVD Sharing" service.


When a CD/DVD is inserted in the computer used to share the CD/DVD, its content will be show under "Remote Disc" on the Mac Mini.