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Photon noise refers to the inherent natural variation of the incident photon flux. Photoelectrons collected by a CCD exhibit a Poisson distribution and have a square root relationship between signal and noise (See Signal To Noise Ratio).

In physics, the number of photons collected by an instrument which are emitted from any incoherent source are distributed according to a Poisson distribution, as long as the average intensity is constant over the bandwidth of the instrument. This is because the photons are discrete and the probability of one photon's arrival is independent of any other photon's arrival. In other words, it is a Poisson process. Since the Poisson distribution approaches a normal distribution for large numbers, the photon noise in a signal will approach a normal distribution for large numbers of photons collected. The standard deviation of the photon noise, which is a measure of the expected difference between the number of photons collected and the average number, is equal to the square root of the average number of photons (source: wikipedia). This wikipedia page has also a nice illustration on this topic.

The noise is therefore directly dependent on the number of photons recorded in a real image. A very bright feature emitting many photons will have little (relative) noise. A very dim feature will look "granular", revealing that not many photons were averaged during its acquisition. This can not be known in advance just by looking at an empty calibration image.

Moreover, the kind of noise in which we are interested is not something intrinsic to the device (that would be another type of noise, maybe from the electronics) but something in the nature of the photons that are averaged. Therefore it also depends on the acquisition time: the larger the exposure, the larger is the amount of photons gathered and the lesser the noise.

See also our wiki page on acquisition pitfalls.