A sump is simply a smaller tank set below your main tank, with water flowing between the two. The sump is a place equipment that might be unsightly or dangerous to the inhabitants of the display tank.
Installing a sump requires three things:
1) The sump itself: Usually a smaller aquarium that sits in the stand.
2) A pump: sends water from the sump up to the main tank through a vinyl hose or PVC pipe.
3) An overflow: this is installed on the display tank and returns water to the sump via gravity. This typically includes a box inside the display tank who's top edge defines what the water level will be in the display tank. Water "overflows" that edge and is sent down to the sump via a hose or pipe. In this way the flow back down to the sump is always balanced with the flow through the pump.
There are two basic kinds of overflows. The first, and best, involves having holes in the glass of your aquarium and the box installed around them. The other way is a hang-on-back overflow that uses a siphon to transport the water in the box to a second, external box. From there it flows into the sump.
Dan