"Live Rock" are rocks that have been in contact with seawater long enough to allow bacteria, animals and plants to colonize them... forming a very complex microecosystem. Both, in "the wild" and in the marine aquaria, Live Rock provides several essential ecosystem services, like: habitat, refuge, substrate, food source, waste cycling, alkalinity enhancing and pH buffering, and landscaping aesthetics.

Most books and websites define Live Rock as "rocks from the ocean that have been introduced into a saltwater aquarium", but we think this definition is not precise enough because it excludes tank-aquacultured Live Rock. Therefore we decided to come up with a more accurate definition:

Live Rock is a non-fluid biogeochemical matrix composed of inert substrate and living cryptic organisms. Live rock is a microecosystem created by the prolonged exposure of substrate to seawater and a source of colonizing organisms.

Lets explain this in plain English...
 
Biogeochemical matrix.-  It is a complex 3-dimensional structure formed by rock, rubble and other inert substrates (geochemical matrix) and by the organisms living on and inside it (biological matrix). The living portion of the matrix is formed by a diverse variety of organisms known as cavity dwellers or cryptic organisms, and includes bacteria, crustose algae (fleshy and coralline), sponges, tunicates, worms, barnacles, snails, amphipods, etc. These organisms often play an important role in the consolidation of the non-living part of the matrix, or in other words, the organisms "glue together" the rubble and rock and hold together the 3-dimensional matrix. The living and non-living parts of matrix are so intertwined that it is logical to refer to it as a whole... a biogeochemical matrix... or Live Rock.

Non-fluid.- The biogeochemical matrix needs to be non-fluid, which means that its size has to be large enough to not be tumbled around by normal currents... that is, it needs to be larger than gravel. When the substrate size becomes smaller than gravel or sand, it starts to move around with currents, behaving a bit like a fluid. Although the chemical properties of live sand and Live Rock are somewhat similar, the organisms living in soft sediments are fundamentally different from the organisms on rocky substrate. Live sand and Live Rock have very different ecology.

Colonizing organisms.- These are bacteria, larvae, propagules and wanderers that can colonize bare rock. They are the "seeds" that will first start the colonization of the non-living matrix. These colonizing organisms are easily found in the ocean nearby existing coral reefs or rocky areas. However, colonizing organisms need to be introduced using "seed rock" when making Live Rock in tanks, either in private aquariums or in commercial enterprises that make tank-aquacultured Live Rock.

So... if any substrate is submersed in seawater containing a "seed" source of bacteria and cryptic organisms (ocean, aquaculture grow-out tank or aquarium), it will eventually get colonized and turned into Live Rock.