Auxiliary heat is the backup heat source a heat pump turns on automatically when it cannot meet the thermostat's demand alone, usually electric resistance heat strips in the air handler. It also runs during defrost cycles. Emergency heat is the manual thermostat setting that locks out the heat pump and runs only the backup source.
Why it matters to you
Heat strips use roughly two to three times the electricity of a working heat pump for the same heat, so auxiliary heat that runs when it should not is one of the clearest signs a heat pump needs service.
Practical guidance
Seeing AUX on the thermostat on a very cold morning or during defrost is normal; seeing it for hours in mild weather is not. Use emergency heat only when the outdoor unit has failed, and arrange a repair rather than running on it for weeks.