If you have a multi-stage heating and/or cooling system (2 or more stages of heating or cooling) then this means that the 2nd stage (auxiliary stage) of heating or cooling is running based on the calculated need imbedded in the logic of your Braeburn thermostat. If you do not have a multi-stage heating or cooling system then AUX being displayed means that a multi-stage thermostat was installed on your single stage system and you will occasionally see AUX displayed on the screen or the green AUX light illuminated (some models), however it does not affect the function of your thermostat or system.