I did google it and there are two varieties, radiant detection and flame rectification. I cribbed the following from the internet. I understand the purpose of the flame sensor is to verify that when the gas is flowing that it is also burning. Your question of *how* it verifies that a flame is present is described below, somewhat beyond the depth of my understanding.
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There are infra red flame sensors that only need to get a "look" at the flame, but I think you are referring to the flame sensors commonly in gas furnaces and equipment.
These types of flame sensor use a process of flame rectification to sense that the flame is lit, and they must be actually engulfed in the burner flame to function.
Flame rectification uses the fact that a flame will rectify an AC voltage to DC and allow that DC current to flow through a flame to detect a flame.
Commonly, an AC voltage is applied to the flame sensor with a wire coming from the ignition module. When the flame sensor is engulfed by a flame, The AC voltage is rectified and a DC current, commonly 4-12 microamps, flows from the ignition module through the wire to the flame sensor, through the flame to ground on the furnace chasis.
The ignition control module has a circuit to detect that DC current, and commonly closes a relay when the DC current is detected that verifies that the burner is properly lit. If the burner fails to light or is extinguished for any reason, that DC current disappears and the control module takes suitable action to turn the burner off.
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Flame rods or ionization probes work on the principle that when an AC voltage is applied between the rod and ground a suitable flame and correct placement will cause the AC to be superimposed with a DC component (ie shift the zero axis positive or negative) The flame sensor amplifier responds to this DC component. The magnitude of the DC and hence reliability of the flame operation is determined by a number of things including 1) the rod must be placed in an area where good combustion is taking place 2) The flame must be firmly "anchored" to the burner diffuser which is ground 3)the surface area of the efficient ground compared to the flame rod itself must be in the ratio of 4:1 or better (ie thin rods work best usually made from kanthal.
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