Some HVAC systems support auxiliary heat (AUX) as well as emergency heat (E). 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 electric heat strips to provide the additional heat needed. Some thermostats have an E wire. The E wire controls emergency heating. 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, the system bypasses the compressor and directly accesses the electric heat strip.
For a more detailed description of the AUX and E wires please please see the attachment below.