The Netatmo station itself requires WLAN (in order to be able to send the data to my.netatmo.com). The weather data is not requested from the station, but from my.netatmo.com - therefore 'any' data connection to the internet is sufficient, e.g. 2.5/3/4G, WLAN for SmartPhones, WLAN/LAN for notebooks/PCs etc. (From the SmartPhone, the NetAtmo app or 3rd party apps such as WeatherPro are best used, from the notebook/PC a browser is sufficient).
During installation, you create an account for my.netatmo.com, where the data can be accessed in the form of a dashboard. You also log into the app with this account. You don't have to be at home in the WLAN to do this; access also works when you're on the move.