Jumpfrog is correct.
Probably the most significant benefit to having a sump (aside from getting ugly equipment out of the main tank) is adding more water to the system.
A larger body of water is more stable, always better for the tank inhabitants. It takes longer for pollutants to build up, longer for temp to change, longer to deplete minerals, etc. In the end, much, much easier to maintain.
Also, you can house a larger (maybe better) skimmer in a sump than you could in/ on your main tank. You can also set up things like kalkwasser drips, auto water top-off systems, carbon media bags, etc in or next to the sump.
The sump is a great tool for mechanical filtration and chemical filtration (carbon, poly filters).
Live rock and sand beds are a great source of biological filtration (the bacteria that break down waste that you establish when cycling your tank). For those that do not use live rock, they usually set up a tower of bio-balls in their sump as a substitute. That is why reef tanks usually dont use bio-balls, they just have alot of live rock and vice versa.
Does that help? I hope so.
Good Luck,
-Christine