When the stove is turned on, a sensor generates electricity to its electrodes, causing a spark that ignites a controlled amount of gas. The clicks you hear are from the electric sparks.
Electronic ignitions have replaced pilot lights in newer oven models, because they use less gas than a standing pilot light -- which has to burn constantly. In older stoves, if the pilot light goes out as a result of a gust of wind or malfunction, gas could build up. This, in turn, can cause an explosion when re-lighting the pilot with a match. Electronic ignition stoves do not require a lit match to operate.
The clicking should stop once the flame ignites. If it continues, it could be caused by grease or food blockage on the electrodes or sensors. Alternatively, the spark module may need to be replaced. If the blockage is visible, it can be cleared with a pin or paper clip. If the cause is not immediately apparent, contact a professional.