You apparently have a heat pump system. Auxiliary refers to the electric heat elements (strips). If the outdoor temp is very cold and the heat pump is unable to produce enough heat to maintain the target indoor temperature, the heat strips will automatically activate to supplement the heat pump -- the compressor and heat strips run at the same time.

The heat strips are also used in emergency mode, which is usually activated by a manual switch on the thermostat (meaning you, the homeowner, must engage it). Emergency mode purposely shuts off the compressor and runs only the heat strips, and is used if the compressor/outdoor unit breaks.