I think that when SWAT asks about the weather-station database, it is looking for stations for which you have all the necessary statistical parameters, so that it can generate missing weather values as needed. If you're not working in the USA, you'd need to calculate these statistics based on weather stations in your area -- see the WGEN program (I think it's called that) on the SWAT webpage. I haven't done this myself, so I'm partially guessing here.
The files giving names and locations of specific stations for which you have precipitation and temperature are entered under dialog boxes for those variables.
-- Jim