Some HVAC systems support auxiliary (AUX) heat as well as emergency (E) heat. Auxiliary heat is used when the balance point can no longer efficiently transfer heat from the outside air (usually about 35 degrees Fahrenheit ). A thermostat senses this and automatically turns on the auxiliary heating element to provide the additional heat needed. On some thermostats, you'll see an E wire. The E wire controls emergency heat. Emergency heat is used when the HVAC system is not functioning properly (usually when the compressor is out of service). When you set a thermostat to emergency heat, your system bypasses the compressor and directly accesses the auxiliary heat.
For a more detailed description of the AUX and E wires please please see the attachment below.