Uyuni is a tourist town in Potosí Department, Bolivia, which serves as the main gateway to Salar de Uyuni, the enormous salt flat nearby.
Uyuni is a small town in the middle of nowhere. It originally blossomed as a transportation junction and then as a railroad hub, and though this is still an important aspect, tourism is now its main source of prosperity. What would otherwise be a fairly dull stopover en route between Salta, Argentina and La Paz or Potosí, has become absolutely mandatory on this leg of the gringo trail. The sole reason: salt flats, the world's biggest: the Salar de Uyuni.
There's not that much to do in Uyuni itself, so just plan to stay for as long as it takes you to do your salt flat tour. Spending one night in town before the tour and one night after should be enough, and may even be more than you need depending on your transportation plans.