Flame sensors determine if there is a flame present. Most people think that the flame is sensed by heat. It is NOT. Instead the flame is sensed by a small electrical current sent through the wire going to the rod. From there, the current passes through the actual flame to ground, creating a very small electrical signal (a millionth of an amp) to the ground of the burner. The circuit board measures this signal and says, "OK - I have a flame."

If there is any oxidation or residue on the flame rod, it will create resistance that will prevent the current to flow through. So the flame could be surrounding the flame rod, but the current can not go through because the residue on the flame sensor, is stopping it.  

To clean a flame sensor is a very simple, but crucial part of routine maintenance on your appliance. Remove the flame sensor and simply sand it with a very light sand cloth to remove any oxidation. If there are cracks in the porcelain replace the flame sensor.