The Sweetwater River is an aqueduct built by the people of Braavos to bring drinkable water to the city.
The aqueduct was a necessity to build as the lagoon that Braavos is located in does not contain drinkable water. Whilst it is possible to drink from it, you have to boil the water first. The Sweetwater River brings healthier water from the south of the city. Richer citizens can have it pumped directly into their house, but the poorer people of Braavos collect it from large, public fountains.