Audio Resolution or Sample Rate represent the number of samples taken of an audio signal per second. Think of it as how many times per second a 'picture' is taken of the sound. The number is divided into two parts, usually written like this: "16 / 44.1" or "16 bit / 44.1 kHz"
Sometimes, you may see only the second number: "44.1 kHz". Note that numbers like "192kbps" are something slightly different, called Bitrate.
The first number defines the bitdepth, that is how big the sample, or how big the picture taken is. This effects the Dynamic Range. At 16bit, the dynamic range is a theoretical 96dB, and a 24bit file has a theoretical dynamic range of 144 dB (for comparison, a full orchestra has a dynamic range of about 70 dB). CD's are all 16 bit, though with the rise of downloadable music, 24 bit is becoming a popular format for music. This bitrate is available on DVD and Blu-ray.
The second number is the actual sample rate. This is how many 'pictures' are taken per second. The CD format, which is 44.1kHz takes a sample 44100 times a second. This allows for recording of frequencies up to 22kHz (above the generally accepted healthy hearing range for people). If you are interested in the science behind it, check out the Nyquist–Shannon sampling theorem on Wikipedia.
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