Weather is represented by various types of fully-animated weather conditions in the game, including wind. Much like in real life, adverse weather and/or wind conditions can cause delays and in some cases (and after severe delays), cancellation. A weather station is required to obtain the exact weather forecast, although basic weather conditions can be obtained by viewing the weather/wind animations and sound effects outside the terminal building. A planned feature is to have weather affect operations, depending on the type of weather and severity.
At this time weather conditions are completely random. As the game gets further and further into development, the location of your airport will affect your airport's climate and other factors, although at this time the location of your airport does not affect it.
The weather station is a placeable object that is unlocked from the start of the game. It will tell you the current and predicted future weather for the location of your airport.