A sump is a body of water usually below the tank that houses equipment (heater, protein skimmer, reactors- if used) it also houses carbon and phosphate remover to remove nasty stuff, most will also incorporate a refugium section. The refugium section CAN (but does not have to) house a deep sand bed (aids nitrification but can house critters aswell), we tend to grow a type of macro aglgae in there also that uses nitrogen and other organics for growth thus outcompeting nuisance algaes in the display tank. If you light the sump on a reverse lighting cycle (opposite to the tank itself) it will also aid in keeping the pH more stable, you will have photosynthesis occurring day and night (day time corals, night time macroalgae).
The other advantage to a sump of course is the extra volume of water the sump adds to the tank, it keeps things even more stable. Replacing water after a water change into the sump is beneficial as water pouring onto corals does upset them. Additionally it gives us extra space to add live rock rubble, this increases the filtration capacity of the tank.
Here is a picture of my sump to help you
Water from the tank enters from the pipe on the right, in this section is live rock rubble, the Bubble stop at the rear with a pipe going into it, this contains carbon and phosphate remover, there is also the protein skimmer (the one with a cup on top) which will be upgraded shortly. The water then passes over the piece of glass (called a baffle) into the refugium section, this holds chaetomorpha macroalgae, here micro organisms that are eaten by fish will also proliferate. Water passes throught he algae and underneath the next piece of glass. It will then flow over the next baffle into the return section. I need more live rock rubble here. Water is then pumped either to the bubble stop in the first section or back into the tank. Also housed here is the heater for the tank.
A sump is not necessary, however it is a very useful add on and does also conceal the equipment that would otherwise be in the tank.
A good website for you to read about sumps is Melevs Reef, here is a link
Melevs reef (click on acrylic and DIY) Have a good read on the site, it is full of very good information and of course his tanks are stunning.