I assume you have a heat pump.

It means the auxiliary heat strips, or other backup heat source, have come on because your heat pump can't keep up during the cold snap we are having. It is expensive, but normal considering the weather conditions.

Not to worry (except for for how much the next bill will cost). You can minimize the costs by turning your heat down as much as you can stand.

Need Help.Can i run the emergency mode regularly.Is it costly?

"Emergency Heat" and "Supplementary Heat" both use the auxiliary heating elements, but in different ways.

Supplementary Heat is operation of the auxiliary elements and the heat pump compressor at the same time -- the heating elements supplement the output of the heat pump. Supplementary triggers automatically if the indoor thermostat detects that the heat pump alone isn't keeping up with the heating load ... that is, either 1) the room temp has dropped 1.5 to 2 degrees below the setpoint, or 2) in some cases it works by a timer, the system has been running for a period of time without reaching the setpoint and cycling off.

Emergency Heat is a manual setting on the thermostat that is switched by the homeowner. It shuts the heat pump compressor off and runs only the auxiliary elements, and is intended for "emergency" situations such as if the compressor fails and there's no other source of heat. Emergency can be engaged whenever the homeowner desires, and sometimes is a good idea during wet/freezing weather if the outdoor unit is icing over quickly between defrost cycles ... but yes, it's more costly to run.