The Rim is the edge of the Discworld. It is about thirty miles thick. It's the end of the world, where water continuously falls off in what is known as the Rimfall. Why the water never runs out is one of the disc's greatest mysteries, another being why it falls, and where.
The most notable place near the Rim is the island Krull, whose inhabitants constructed the Circumfence. The mountainous edge of Krull actually sticks out over the rim, so that it is possible to look down and see the stars.