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.
Last edited by TobiSGD; 01-05-2014 at 10:06 PM.
Reason: fixed typos