Even a pilot light needs to be lit from some source. Older pilot lights required owners to use matches, but yours probably has an electrical ignition system. If the pilot light is not working and all your hear are a series of clicks or noises, the pilot light may have become clogged with contaminants. Also, a sharp rush of air or an exploding sound could mean the pilot light is not turned up high enough to ignite the gas properly.
If you have an electrical version, you probably have a prong of electrodes that create a spark that jumps between the two prongs. These electrodes can become misaligned through time or sudden force, which can lead to serious problems for the ignitor. If you hear rapid clicking but the burners do not work, this could be the electrodes trying to create a spark, but being too far apart or in the wrong position.
The thermocouple senses the heat of the pilot light and allows gas to flow into the primary burners when the light is hot enough. If the thermocouple malfunctions, it could lead to ignition issues, such as the ignitor refusing to work, or the "exploding" sound as the ignitor works too late with too much gas. A failed thermocouple could also lead to the furnace turning on and off quickly as it receives conflicting signals.
If it sounds like the burners themselves are turning on and off rapidly in a series of clicks, the problem may be clogged fuel lines or (if you use oil) a clogged fuel filter. This occurs because of age and contaminants. The thermocouple also may be responsible if it is directly shutting off the gas supply every time the system tries to turn on. You may need to clean or replace the burners if the fuel lines themselves are the problem.