My colleagues and I actually wrote a textbook, that is entirely FREE for you to download. Google the Trace Analysis Research Center Dalhousie University. Click the education link to download a copy of "An Introduction to Analytical Chemistry"

Noise can be assumed to be random, and follow a standard normal distribution (bell shaped curve). A signal to noise of 3 means 3 standard deviations above the mean (baseline). A random spike in the baseline with S/N above 3 only happens about 5% of the time. So basically, it's a way of picking how sure you want to be that your signal is real, based on 95% confidence.