dynamic rangeThe Dynamic Range is the maximum contrast a camera is able to reproduce from the point the camera reaches it’s maximum output level (saturation) down to the point where the signal is just as high as the noise level so that noise and signal cannot be distinguished anymore D = S(max)/σ(dark). It is measured using a gray scale target with a contrast greater than the expected Dynamic Range of the camera under test.

The reported value for the Dynamic Range can have different units that should not be confused. One unit can be the contrast ratio given by the transmission of the gray scale at the point of saturation and the point where the noise level is reached. It usually is reported as a ratio e.g. 1000:1. This unit can be transferred into density difference by using the log value of the number before the :1. In our example it would be D = log(1000) = 3 densities. By knowing that each f-stop reduces or increases the amount of light by a factor of 2 that equals to log2 = 0.3010 or app. 0.3. If the densities are devided by 0.3 you get the number of equivalent f-stops which is equal to exposure value differences.

Dynamic range units conversion contrast densities f-stops
contrast 1 Log(c) Log(c) / 0.3010
densities 10^d : 1 1 d/0.3010
f-stops 10^(f * 0.3010) : 1 f * 0.3010 1

noiseNoise in images is an unwanted modification of the signal due to physical behavior of the camera and the parts it is made of. Some of the noise may be randomly distributed and some may show a regular structure. It often is differentiated in a temporally varying part and a fixed part. It is usually expressed as the standard variation of the signal coming from a uniform original like a gray patch using the Greek letter σ. Often times a value called signal to noise ratio (SNR) is used that expresses the relation of the signal level and the noise value at that specific signal level: SNR = S/σ. This expression does not have a unit.

In electronics the SNR is also often expressed in dB. The SNR mentioned above can be converted into dB using: SNR[dB] = 20 log(SNR)

Background information can be found here: http://en.wikipedia.org/wiki/Decibel

Nonlinear Systems
The signal to noise value is calculated the above-mentioned way for linear systems. For cameras that use a non linear tonal curve the formula needs to be modified because at a given signal level the noise level being the standard deviation has been modified by the incremental gain (local steepness of the OECF) therefore the noise needs to be corrected by dividing it by the incremental gain (g). 
This leads to SNR = S/(σ/g) => SNR = Sg/σ

Details are given in ISO 15739.