A sump is another tank of water usually under the main reef aquarium that can house various forms of mechanical, chemical and biological filtration. It can also be used as a refugium.
A sump will increase the water volume of the reef system and having the larger volume makes the reef aquarium more stable. Water parameters like PH, salinity, Carbonate Hardness and Calcium levels will change more slowing and be easier to manage. Adding a sump can be like taking a 90 gallon aquarium and making it a 130 depending on the size sump you are able to use. This additional water volume will also dilute waste in the aquarium and improve water quality.
Having a sump provides space for your equipment, algae and more live rock if need be. A space with algae can be used as a refugium where the smaller organisms can grow like mysis shrimp, copepods, and amphipods.
To create a refugium in your sump you will place live rock and macro algae in a section that is partitioned off. Some people will also add substrate. I prefer not to add substrate so I can siphon out detrius that will build up.
Having a sump allows you to place your skimmer in the sump instead of having a hang-on skimmer that can over-flow on your floor. This is a big deal if you have ever had smelly skim-mate end up on your floor.
When I set-up a sump for most saltwater aquariums, I will make the sump a big as space will allow. I add an in-sump skimmer, carbon reactor, phosphate reactor, calcium reactor, chiller, and more live rock. If you have a refugium area you can add macro algae and substrate. I use a phosphate reactor to keep phosphates down low enough that macro algae does not grow. If your reef is mainly soft corals, they will not grow as well with phosphates down this low and the use of algae will be better.
If I set-up a sump with macro-algae, I will light it 8 to 12 hours and on the opposite lighting cycle of the main reef aquarium. If you light the sump for 24 hours the algae will not grow as fast than if you give it a rest period. Faster growing algae will also be better for nutrient export.
Having a sump for saltwater aquariums has so many benefits over not using one that if given a choice I always use a sump.