I'm just barely beginning to get the basics about Mint 16 Petra Cinnamon 32 bit I've installed. My question is about the Software Sources category. I've done some searching about this but I can't seem to get good basic info suited to a beginner like me.

I see listed two default Official Repositories, main (petra)... http://packages.linuxmint.com and base (saucy)... http://archive.ubuntu.com/ubuntu. PPAs and Additional Repositories are blank and Authentication Keys shows Ubuntus Extras Archive Automatic Signing Key and Seiko Epson Corp. (my printer, I presume).

What exactly are Repositories, PPAs, and Authentication Keys? Should there be anything listed under PPAs and Additional Repositories?

Unlike Windows, where you usually download software form the web and install it manually, most Linux distributions have a central software repository, containing software that is configured and tested for your specific distribution. In your case, with Linux Mint, you see two repositories because Mint is based on a different distribution, Ubuntu. Therefore you have the base repository pointing to an Ubuntu server and a second repository, containing software written specifically for Mint, pointing to the Linux Mint servers.

If you update your system or install software a security process takes place, where the packages that are downloaded are verified with the authentication keys, to make sure that no unauthorized third party has altered those packages, for example to hide malware in such a package.

In addition to the official distribution repositories there is a mechanism in place for your distribution that allows to install software from 3rd party repositories, so called Personal Package Archives (PPA). While many trustworthy PPAs exist anyone can setup such a PPA, so handle with care if you enable a 3rd party PPA.

By default those entries for additional repositories and PPAs are empty.

Thanks. I have spent a lot of time "googling" for explanations about this. Your response was the all-time best for a newb.