A campaign is the world beyond the adventure, the cities and forests and coastlines and kingdoms of the fantasy world.
The players will almost certainly want their characters to explore wildernesses, visit cities, and do all sorts of things in the fantasy world. At the beginning of the game, you might want to sketch out a map of a single village (as a starting point) and some of the surrounding area. (The location of the first adventure—a dark forest—perhaps?) As players move their characters around from adventure to adventure, you can expand the little map into an entire fantasy world—with continents, kingdoms, and great empires at your disposal.
If you want to take a shortcut, you can set your entire campaign in a fictional world created by the author of one of your favorite fantasy books. Most of these have maps, and the author has already created the details and the feel of the world for you. The worlds of Conan’s Hyboria (Robert E. Howard), of Elric and the eternal champions (Michael Moorcock), and of the Dying Earth (Jack Vance) are popular fictional settings ready for gaming. Indeed, publishers have already created pre-packaged campaigns for all three of those examples.
Once the players decide to adventure beyond the dungeon, you’ll have to expand your map a bit, and perhaps make plans for the kinds of monsters the party of adventurers will encounter. These adventures might include traveling to another dungeon based on rumors that a great treasure is there, piracy on the high seas, exploring the coast in a merchant galley, dashing to the rescue of a village besieged by an orcish tribe, or hunting bandits for bounty money. The possibilities are endless, and since the party’s direction is up to them you will never quite know what they’re going to do. (This is why it’s a good idea not to try to plan for the campaign’s expansion until it starts to happen.) Most referees create encounter tables for wilderness travel, using the monsters on this site.