Your furnace is meant to cycle on and off when the thermostat triggers it and when your air reaches the desired temperature, respectively. Rapid cycling occurs when a furnace turns on but shuts off far before your temperature is reached. The rapid cycle can be caused by a variety of factors, but the cause is sometimes found in a couple of electrical components.
Here are a couple of the electrical problems that can cause rapid cycling in a gas furnace, which despite its name, does still partially rely on electricity for operation. If you don't have any electrical experience and don't own the proper testing tools, leave the checks and fixes up to a qualified furnace maintenance service service.
The flame sensor is an electrical device that is located near the burner assembly and checks to see if the pilot light is lit. If the pilot light is on, the flame sensor sends a signal saying that gas can enter the system for lighting and heating. If the pilot light is off, the sensor sends a signal, shutting off the gas and stopping heating.
A dirty or malfunctioning flame sensor can fail to consistently recognize the presence of the pilot light. Your furnace might still kick on but when the flame sensor stops "seeing" the light, the furnace will shut back off again.
You can check the flame sensor for dirt by turning off all power to the unit, opening up the back, and locating the sensor using your owner's manual as a guide. Clean off any surface dirt with an abrasive kitchen sponge. Try your heater again and see if it works.
Still cycling but you think the problem is the flame sensor? Call in an HVAC tech for a replacement part.
The pressure switch is another type of sensor. Instead of checking for the pilot light like the flame sensor, the pressure switch checks for the airflow that's necessary to keep the flame lit and the ignition system in operation. If there's not enough air, the switch opens to let in more air. If there's enough air already, the switch closes to prevent the system from getting too much air, which would extinguish the pilot light.
A malfunctioning pressure switch can close before there's enough air in the system, which can cause the ignition to fail or die out quickly. If you have a multimeter, you can check the continuity of the pressure switch using your owner's manual as a guide. If you don't own a multimeter nor know what one is, you should call in an HVAC tech to help out. Visit http://calldoctorfixit.com for more information.