Ok,
Base rock is just the dead rock that is sold on the shelves at the LFS, it is dry, isn't in a tank yet, and sells for 1.99-2.99/lb. There are no living organisms in the base/dead rock. Live rock is the rock that they keep in a tank somewhere and if it isn't cured will be very brown! But most LFS's keep some cured live rock around and is usually about 5.99-8.99/lb. I wouldn't pay more then that ever for live rock!
Hope this helps!