A sump is essentially another tank/container remote to your display tank. It gives you additional water volume, a place to hide unsightly equipement such as heaters and skimmers and makes for and easier water change if located down low. Water is drained from the main display tank and enters the sump and is then pumped back to the main tank.
Live rock is rock with life such as coraline algaes and encrusting corals and small critters. Reefs are comprised of rock and sandy areas that are homes to an abundance of life such as corals, anemones, clams, sponges etc...
A skimmer removes dissolved organic compounds from your water to keep it clean. It produces small air bubble which causes the DOC
to attach and produces a foam of unwanted waste. The waste is collected and dumped.