Backup heat — also called auxiliary or supplemental heat — is the secondary heat source that supplements a heat pump when the outdoor temperature drops below its balance point and the heat pump can no longer meet the home's full heat loss on its own. In most installs it is a bank of electric-resistance strips inside the air handler; in a dual-fuel system it is a gas furnace instead.
Electric strip heat has a COP of about 1 — every unit of electricity becomes one unit of heat, with none of the multiplier a heat pump provides. That makes backup heat two to three times more expensive to run per unit of heat than the heat pump, so a system that leans on it for many hours each winter quietly erodes the savings that justified the heat pump. The goal of good sizing and (where the climate demands it) a cold-climate model is to keep backup-heat hours low.
It helps to know the two modes. Auxiliary heat runs automatically alongside the compressor when extra capacity is needed. Emergency heat is a manual setting that runs the strips instead of the compressor — meant for when the heat pump itself has failed, not for everyday cold. The DOE also warns of a common wiring fault that fires strip heat whenever the thermostat is bumped more than a few degrees, regardless of outdoor temperature; if your electric bill spikes in winter, have an installer confirm the aux-heat lockout is set correctly.