This is very simple. Bear with me here - an note I am using "dB" in a very relaxed fashion.
Noise is always present, as is the signal. How loud is the signal, how loud is the noise?
For digital, you need a signal to noise difference of exactly what is needed so the dac or whatever works. More is simply overkill. It will work, or it will not work. If it works the signal is perfect. (Side note: Clocks are so precise these days, that external clocks would probably introduce timing issues - unless you are in a studio and need to sync - then be happy if it works)
Analog signal to noise is a bit different, because we can actually hear the noise. Tape hiss for instance is a great example (not of snr, but hey, bear with me) to use because many have heard it. -60dB noise floor (tape hiss) and +6db recording level, then S/N ratio is 66dB.
If you have very low musical signal, lets say a single, soft plucking guitar at a distance. Its amplitude converts to 40dB. So you have a difference of 20dB. This is a problem.
If you have a loud signal, lets say an orchestra playing full on) at 0dB (reference level), tape hiss is in all accounts "unhearable".
So again, its the dosage that matters.The ratio of the sound intensity that causes permanent damage during short exposure to that of the quietest sound that the ear can hear is greater than or equal to 1 trillion. Source: National Institute on Deafness and Other Communications Disorders (National Institutes of Health, 2008)
You may feel volume as a smoothly slideing scale of 1 to 150, but it is not true: Decibel is a logarithmic scale. Do you understand what that means? 1 isn't 100 times lower than 100.
"Twice as loud is what?"
- a loudness level of about +10 dB
- Side note: double the sound pressure means 10 times increase in power. Your speakers can do 96dB with 10 watts? you need 100 more to reach 106dB.
With this new found information: If you have a noise of 50dB, and a signal of 70dB (ie 20dB SNR) - how much louder is signal? Twice as loud? 4 times as loud? Something else?
If you have a SNR of 80dB: How much louder than the noise is the signal?
If you sit down and calculate it, you will understand.
A well complied source:
http://www.animations.physics.unsw.edu.au/jw/dB.htm
Edit: I didn't see who the OP is. I made the for you relevant part of my post BOLD