the term live rock simply means that there are things living on it. the primary organism we want on our live rock is bacteria and obviously you can't see that. another common organism we like to gow is coraline algae which is not like most algaes in it is hard calcium skeleton and is usually pink or purple encrusting the rock. other things that grow on rock that are desireable are ast. tube worms and sponges. on some rare occations corals, bivalves, and even tunicates will be present.
live rock can also have present on it pest organisms like undesirable algae - like hair or valonia. pest anemones like aptasia and majanio also are frequent.
many sorts of small crustaceans and sometimes echinoderms also show up.