Shot noise, or the random noise in the target "signal" (Read: target image) is a reflection of the randomness of the photon count being received.
If we count the number of photons received over a period of time they will not arrive at the same rate.
Our first count may be 90, second count, 110, 102, 115 etc etc.
This spread of numbers approximates to a Gaussian distribution curve, also called a normal distribution curve.
https://en.wikipedia.org/wiki/Normal_distribution
The possible error +/- (the "noise" in our signal) associated with a 68% probability (1 sigma error) is sqrt(signal)
This has been adopted as an acceptable measure of the random "shot" noise.