Looks like most of the basic ideas are here. Now its just a matter of piecing them together.
A "sump" is a tank or container that sits under your display tank. your sump usually acts as your main, if not only, form of filtration with either a wet/dry or submerged media system. Adding a sump offers many benifits including a huge amount of media space, increased volume of your water column (helping to stabilize your water parameters), space to keep equipment (like your heaters) out of the display, and the ability to completely customize your filtration to your needs.
a basic sump filter consists of 3 sections. The first is the filter portion. an overflow from your display tank drains water into this section which holds all your bio-media as well as a layer of mechanical media to filter out detritus and debris. The second section is a holding area for your equipment, and the last section houses your return pump which pushes the clean water to your display. (in advanced systems there can be other additions like a refugium, algae scrubber, FBF, auto top off, etc.)
The water flows out of your tank via a overflow system. This can be achieved by drilling your tank and adding bulkhead fittings, buying a pre built overflow box, or my personal favorite, DIY.
You can build an overflow out of PVC pipe for only a couple of dollars. Is cost effective and works like a charm.
The overflow system will drain excess water from your tank into your sump, where it will filter through the first section, be heated in the second section, and finally returned to the tank by the pump n the last section.
I hope this has helped to give you an understanding of the basic functions of a sump system.