Live sand/rock is sand and rock that is alive with all kinds of stuff. Obviously, the sand/rock itself is not alive, but they contain lots of microscopic creatures that help keep a tank in balance. It is typically taken straigh from the ocean, or from an well established tank dedicated to LR/LS. Live rock/sand has the bacteria you need to keep your water stable, but often times it also has fragments of corals that can grow in your tank. Good stuff to have for sure.
Dead sand/rock is just plain old sand/rock... none of the good stuff, just dry rock or sand.