Live rock is the calcium carbonate skeleton of dead coral which has been re-inhabited by a multitude of microscopic (and some visable) plants and animals. In nature, a quarter of the oceans animals rely on the coral reef at some point in there life for food, shelter, etc. It's the corals skeletons that provide a complex structure that allows for this ecosystem to be the most bio diverse on the planet. In our aquariums, coral skeleton is a good surface for growing more microorganisms which keep the water chemistry in balance and accomodating all the other biology which takes root on a natural reef. Snails and urchins and hermit crabs crawl on and clean this natural surface and reef worms and sponges will grow into it but will not grow well on plastic decorations for example.
Diversity of microorganisms in a tank is a good thing, bacteria and other micro-organismsworms as well as worms and sponges act as a nutrient buffer (they eat wastes and recycle organic molecules) and help stabilize the tank. These organisms will come as you get new live rock, live sand, invertebrates, and pieces of coral.
Most aquarists hoping for a successful reef aquarium choose to decorate their tanks with live rock or base rock, which is just coral limestone (CaCO3). There are a few reasons people like using limestone rock for their substrate. When you use all calcium based rock everything tends to match. The rocks all age similarly and sedentary animals and plants which grow onto them, the corals/worms/coraline algae, grow evenly and consistently. In an older tanks everything looks normal, natural, and harmonious.
Don't let a store convince you that you need 1 pound or more of live rock per gallon. It depends on the density of the rocks, the shape of your aquarium, and the ultimate height you want for your rockwork considering fish swimming space and if you are planning to grow tall corals. Also, buying base rock or dry calcium carbonate rock and putting that as 95 percent of your tank is actually safer because there is less potential for dead/dying organisms to foul your water and less chance of introduction of parasites or diseases. The shapes of the big base rocks are usually less desirable and are often more dense so live rock might make sense economically. Anecdotally, difficult to keep corals (specifically small polyped stony corals in the genus Acropora) are often kept more successfully and sooner when more live rock is used initially. My theory is that it seeds the tank with more diverse microorganisms which, when they start reproducing, feed the filter feeding corals. Wholesale live rock costs 1.50 to 2.25ish a pound and the fact that it's marked up 400% concerns me a bit when it's pushed on customers like an essential. The colors of things like sponges and macroalgaes are nice initially but again, all of the organics on it have the potential to die soon after reaching your tank
Live rock recently arriving from the ocean should be "cured". This means that the rock is put in clean salt water, aerated, and all of the organic debris from the dead animals and plants are allowed to rot off and hopefully the live animals then are allowed to start using that nutrient. It's important to watch that the water doesn't get too murky as that would make everything diue. This process takes however long it takes, usually a safe time to wait is 2 weeks. The "smell test" is a good indicator of how new/fresh the rock is. If it smells like rotten eggs it's too early as you don't want that decomposing anaerobic material nutrifying your tank (unless you are jumpstarting a new tank and just use a few pounds). You want the rock to smell like a healthy low tide, "seaweedy" and crisp. If rock sites in vats too long, especially if it's burried under other rock and doesn't get light, it loses most of it's diversity.
I am a big fan of diversity of microorganisms in a tank, things like worms and sponges make a buffer to nutrient and help stabilize the tank, but honestly these will come as you get new corals and small bits of rock. Probably the most important thing right off the bat with the rock is the shape. If buying live rock from the store, ideally you want curvy rocks with lots of holes that has been in a well aerated system, near the top where there's light,has been in the water for a few weeks, doesn't smell like rotten eggs, and has some coralline algae/sponges/worms growing on it.
You want to minimize the amount of dead space for detritus (crap) to accumulate. Do this by minimizing the amount of rocks/decorations that touch the gravel and by not putting big walls of rock in front of your powerheads and outflows. The more rock that is touching the bottom, the more of a chance that you have to accumulate deep pockets of nutrient which may be released if the rocks move or a sand shifts. While not generally a major danger, an avalanche at some point may reduce water quality to a point which could detriment coral. The irony of this is that to elevate more rock off of the bottom usually means that your structure is more precarious and likely to topple. There are reef safe epoxys which can be used to fortify live rock structures underwater.