Twoflower is the first tourist Discworld has ever seen, since he's the only person to have had the weird idea to see the world simply for the sake of it.
He hails from the Agatean Empire on the Counterweight Continent, a place where gold and other rare oddities are in such abundance that his two thousand rhinu amounts to a pittance there, even if it's enough to make an Ankh-Morporkian rich for several lifetimes. Fortunately for his vacation, there are plenty of Ankh-Morpork citizens who would like to be settled for life.
Twoflower is a hopeless romantic. As a child, he grew up reading stories about heroes, dragons, and adventures before he was bound to an apprenticeship with an accountant, and later a career as insurance salesman (3.12.24). Then one day he decided to go on a tour of the world to see all the stuff he'd read about in his books or heard from sailors' tales.
Rather than growing disappointed at reality, Twoflower discovers it is "just like [he] imagined" (1.6.3). His view of the world has become rose-tinted, entirely based on all those stories.
As such, he sees the good, beauty, and adventure in everything. When Rincewind describes a village as "fever-ridden and tumbledown," Twoflower sees it as "[q]uaint" (2.1.2). While witnessing a Morporkian bar fight, he claims it is "better than anything [he'd] imagined" (1.20.15), rather than a hazard to one's ability to live. His worldview is so romanticized by the stories, that he expects forest shelters to include a "gingerbread house" (2.2.4) as a mainstay.
Twoflower represents us, the readers of fantasy literature. If you think about it, the typical fantasy world is a pretty awful place to live. The potential hazards to one's life include misappropriated magic, terrifyingly large beasts, and sword fights around every other corner. Yet we read these stories—we tour their worlds, so to speak—because we see a wonder and romance in them that we feel is lacking in our day-to-day lives. This is probably twice as true if you happen to be an insurance salesman.
Twoflower's naïveté mirrors our naïveté when it comes to how these fantasy worlds would really work. His desires parallel ours. At the novel's conclusion, Twoflower boards the Potent Voyager and exclaims, "Worlds. The whole damn sky full of worlds. Places no one will ever see. Except me" (4.17.41). This is a perfect example of what we're talking about: The worlds Twoflower talks about represent the various worlds of fantasy literature, and his desire to tour them symbolizes our desire to read about them.
Twoflower is the reader; the reader is Twoflower.