In order to demonstrate any signal accurately it is important to know the noise containt in the signal. Thus, a fundamental measure is the ratio system which in this case is SNR.
In communication system: The signal-to-noise-ratio, the bandwidth and the channel capacity is calculated by Shannon-Hartley theorem. SNR can be calculated as th ratio of variance of signal and noise. In Image Processing: The SNR is also used in the physical measure of the sensitivity in image processing. Where SNR can calculated as the average value of foreground to the standerd deviation of background.