Yes, I know which button it is although it is 2nd from the left on right-hand drive cars. However that's the only reference to Wide Air Outlet in the manual that I can find. There is no explanation of what The Wide Air Outlet is, where it is or what it does.
That's it. I found some information on another forum. It uses the vents across the entire width of the dashboard (I thought the ones without controls were just for show) to maintain temperature without blowing air so you don't get the blast of air with high speed fans that you get using the normal left/right vents. I guess if cabin temperature is much lower or higher than that required you would need the fans to reach the desired temperature and then switch to Wide Air Outlet to maintain temperature.
My wife will love this as she is always complaining about the ferocity of the fans
Shame Audi couldn't be bothered to put an explanation in the manual.