System Diagram of a reef aquarium -- The Big Picture

Simply put, you need a combination of two tanks. One for the animals and one for water treatment.  The upper tank is often called the display tank (DT) . The lighting system hangs over (or sits on) the display tank.  Light and water -- the two main ingredients.

Saltwater, liverock, and the animals (fish, corals, etc.) are placed and arranged in the display tank.

Water drains via an overflow from the display tank down to lower tank (often called the "sump") where it is treated and then pumped back to the display tank in a continuous loop. Other devices (protein skimmer, chiller, heater) to aid water treatment are often inter-connected in the sump area, or if a separate room is available, the "fish room".

Like a swimming pool setup.  A place to swim and an area for water filtration, equipment, and treatment.

 
A space directly below the display tank is often used for the sump and enclosed to hide from view the sump and related water treatment equipment.  The cabinet (or stand) also provides a top shelf to support the display tank.