A live install means you run the OS (Operating System), in this case, Mandriva directly from the CD. You don't have to install the OS on your hard drive. You just stick the live CD in your CD drive and it'll boot up the whole OS.
Most ppl. do this before intallin' the OS permanently onto the hard drive, so they get the feel how the OS looks and works
Yes, Mandriva is free of charge
http://www.mandriva.com/en/download/free
i haven't tried Mandriva but it should be great because it's the 7th most popular Linux distro (I'm usin' Ubuntu). Here's a review of Mandriva Spring 2008
http://blogs.techrepublic.com.com/opensource/?p=249
And this is the summary of Mandriva Spring i got from the article above
"Display: Works perfectly.
Wireless: Works perfectly.
Sound: Works perfectly.
Hibernation: Works for the most part but because of the Live nature the laptop doesn’t want to fully hibernate.
Performance: Outstanding (blows away the currently installed gOS).
Installation: Quirky but simple."