Presumably it works the same way as any other electronic weather station - a temperature sensor and a barometric pressure sensor. As far as I can tell, the only difference is in the way that it displays the result.
The weather station contains a transistor that is 'pressure sensitive'. In weather forecasting it is the changes in atmospheric pressure over time (trend) that give an indication of what's likely to happen. The weather station measures these changes and displays the (possible) weather prognosis. The results are always a generalisation, since there are other factors involved that the weather station can't take into account. Scroll down to ''General Rules...'' here, to see how pressure changes affect the weather...