SNR is also known as Signal to Noise Ratio. If you would alter the SNR, you can already expect that this will also change the bandwidth. This means that they are related to each other. Take note that the presence of noise will make it harder for the other signals to be detected.
SNR is important because the main goal of people is to see how clear the signal is. It would be easy for people to know if a certain amount of noise will be enough to disrupt signal or not. There are times when the a certain amount of noise will be tested just to see if signal is still clear enough.