Systems with an igniter, often do not have a standing pilot, and it goes from all off to main burner on. Once that completes, after a very short time, a flame sensor will determine if it actually lit the burner. If it didn't, it will go into post-purge mode to vent the gas buildup before it will try again after a delay. Most will only try that sequence a few times, then trigger a fault light waiting for you to reset it. There often is at least a couple of other safety sensors to verify things are working properly like maybe a vacuum sensor to determine if the air supply is viable without restrictions, a high temperature cutout in case things got too hot, etc. Any safety interlock must also be working for the system to eventually generate heat.
A flame sensor can be made several different ways: optical (could be dirty), or thermistor (electrical resistance changes with temperature), and probably others. The sensor must not have become displaced from its properly location and the leads to the control board must be intact without breaks or corrosion.
Main burner ignition depends on first the igniter actually generating a spark, then the gas valve actually opening with adequate gas pressure and volume available, then the flame sensor to allow the burner to remain on until the thermostat is satisfied. If you hear a clicking, you have a spark type igniter...there are other types, generally glow (electrical resistance - sort of like the heating element in a toaster) that get hot enough to ignite the gas without a spark, but those don't generally make clicking sounds.