They work as photoplethysmogram:
Because the skin is so richly perfused, it is relatively easy to
detect the pulsatile component of the cardiac cycle.
Basically the light flash measures your heart rate.
The change in volume caused by the pressure pulse is detected by
illuminating the skin with the light from a light-emitting diode (LED)
and then measuring the amount of light either transmitted or reflected
to a photodiode.
Example: Pulse Oxemitry
a phone is not a proper photoplethysmograph, so the realistic
achievable accuracy is likely dependent on a number of factors,
including camera performance, proximity of the illuminating LED to the
camera lens, and the algorithm used to extract the pulse from the
all photoplethysmographs are very sensitive to mechanical movement. It
is essential that you hold your finger as still as possible, and avoid
moving the phone relative to the finger.
This site did a study on app proficiency and they did show that they are highly accurate most of the time, but can vary in reading by being a couple off the mark:
GP’s normally instruct adding or subtracting ten from the reading of a
digital device depending on the trend (if your reading is normally
higher than average, add ten, if it is less than average, minus ten).