Signal to noise ratio is the ratio of signal (what is meant to be heard, like music) to noise (interference from things like the power supply or your microwave oven that mess up the audio signal). If the signal (your CD track, for example) was recorded poorly, there will already be noise and distortion in the recording that cannot be fixed by good player/receiver/speakers. Typically, though, professional audio recordings are quite good and it is usually on the playback end that noise gets introduced. That's where a high quality playback device (like the Xonar) comes in. SNR is one of many measurements that can determine how clean a recording is played back, but it's a popular one.
Theoretically, every time you play a sound on your Xonar it's being played back with the specified SNR from the Xonar itself. Once the signal exits the sound card, you're at the mercy of the amplifier and speakers.
SNR applies to sound, but it also applies to any field where one wishes to measure the ratio of some thing that is desired to some kind of interference.
EDIT: for a good example of the production pipeline, think of a football player during a game. At every stage of the game, his jersey is going to get mud slung onto it. The amount of mud that gets slung onto his jersey is akin to the SNR -- the more mud on his jersey, the lower the SNR, i.e. what you intend to be there is blotted out by interference. If there's enough mud slung during the game you won't see his jersey by the end; it'll be all covered in mud. Just like mud gets slung around from the start of the game to the finish, the same is true with signal noise. Noise can be introduced at the recording stage, encoding, decoding, transport, playback, etc. stages. If there's enough noise at any one step or combination of steps, the sound quality gets really bad. The Xonar's high SNR means that it is not going to sling much mud onto your music.
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