In case you haven't been told, newer aquariums go through a series of algae phases, which include things like diatoms (good, normal, food for bacteria), cyanobacteria (normal, undesirable, can be frustrating to remove), detritus (normal, made up of fish waste or decaying food), or lastly dinoflagellates (awful, something you'll never want to deal with).
If you have good flow in your aquarium and a healthy clean up crew to keep the sand stirred, your substrate should look relatively clean. Nassarius snails are good critters that move through the sand, sand-sifting gobies filter sand through their mouths/gills keeping it loose (and in piles that may even cover up corals you care about), serpent starfish are good while sand-sifting starfish are not good in a reef tank, and kole tangs will snack on things off the sand.
A healthy sandbed should have all sorts of cool critters living in the substrate, some of which is food for pod-eaters like mandarins, others that will eat decaying matter. You may observe a variety of different worms: bristleworms, spaghetti worms, polychaetes and spionid worms. You may even note some tiny brittle starfish in the sand, if the wrasses haven't noticed them first!
Additional reading: Clean Up Crew critters