urpmi is a commandline tool developed by Mandriva to make installing and updating software easier. It is based on the RPM system, and automatically handles dependencies.
Some more detail on using urpmi over at the URPMI tutorial.
urpmi gets the software packages from sources (mirror servers containing the rpm packages). You need to configure urpmi on your machine to point to sources you want to use. An easy way to do this is with easyurpmi. Make sure when configuring sources, you match the exact version of Mandriva that you are using.
There are different types of sources.