When divers pull rock off the sea bottom, it's often covered in sponges, algae, hard and soft corals, anenomes, etc. Most of this stuff cannot survive the shipping process, and lots of it is chopped away on the spot. Rock is heavy, therefore expensive to ship. Water is, too. Nobody's buying the water at the other end of the line, so most places don't ship it. Rock is usually shipped damp, not wet, and exposed to air.
By the time a piece of rock comes out of the shipping crate, only the hardiest things have survived. Anything else that was still attached when it went into the crate is dead or dying. We call this uncured live rock. Responsible re-sellers will place uncured rock into a large container of water with a powerful protein skimmer, and leave it there for weeks before selling it. When all the dead stuff has been processed, and the rock has re-built healthy populations of nitrifying and denitrifying bacteria, we call it cured live rock.
{Nit-Picking} Adding uncured live rock to your existing tank will disrupt the cycle that is already running in your tank, but it won't cause a nitrogen cycle to occur. Here's why:
When we say a tank is cycling, we mean that it is establishing a nitrogen cycle. When we say that the cycling process is finished, we don't mean that the nitrogen cycle in the tank has stopped. Far from it. We really mean that the cycle is well-established and running smoothly.
So, saying that adding uncured rock to your tank will cause a nitrogen cycle... is ridiculous. The nitrogen cycle is already running, and it will keep running. Tossing a bunch of ammonia-releasing dead organic matter into the tank just throws the cycle out of balance. There's more ammonia than the current crop of nitrifying bacteria can eat, so they reproduce wildly to catch up. A little while later, all the excess nitrate they've produced reaches the denitrifying bacteria, and it's their turn to play catch-up. Eventually the ammonia level drops, a bunch of bacteria starve, and the populations shift back into balance. {/Nit-Picking}
If you want absolute maximum diversity, look for rock that is shipped immersed in saltwater. It's expensive, but you'll probably see things that rarely survive damp shipping. At least one of RC's sponsors, Tampa Bay Saltwater, ships aquacultured rock in saltwater. There may be others.
To cure uncured live rock, put it in a container of saltwater, hook up the best protein skimmer you've got, and wait. If there are photosynthetic organisms on the rock that you want to keep, put a light over the container. If not, don't bother. A couple of water changes and weeks later, the ammonia and nitrite levels in the container will drop. When nitrite is zero, and nitrate is real low, you've got yourself some cured live rock.