Imagine someone is talking while you are trying to listen to your favorite music. That is a perfect example of background noise compared to the loudness of music. Now imagine your amplifier is the one doing the talking in the form of “hiss” coming out of your speakers while you were listening to the music, that is precisely what signal to noise ratio is. If you put your ear up to a speaker when it is being powered, even when the music is not playing you will hear this small amount of “hiss”, that is what we consider the noise floor to be. All amps will produce some degree of this but with any good amplifier you should not be able to notice this hiss at any listening distance away from the speaker. So SNR is this ratio of signal strength in relation to the amount of background noise and is typically represented as a number in db. The higher the number, the less noise there is going to be.
In general, I personally consider anything above 100db SNR to be quite good.