Photon noise (or shot noise or Poisson noise) is variation in the measurement of electromagnetic radiation due to its quantum nature, i.e., if the number of incoming photons is small, the rate at which they trigger a detector can vary through pure chance. The concept was introduced in 1918 by Walter Schottky.
In astronomy, clear, unambiguous observation of distant objects may be limited by photon noise. The noise in a finite observation follows a Poisson distribution, which with enough photons, is virtually Gaussian (i.e., the normal distribution described by the Gaussian function). However, astrophysics is getting what you can out of however small amount of data you can acquire, so disentangling the photon noise (and thermal noise) from the signal is of interest, and efforts are made to model the various components mathematically to untangle signal from noise. The term shot noise level (or Poisson level) refers to the degree of photon noise that is contributing to the resulting signal/noise mix.