Well, since you asked (and you did), I am going take you to school. There are TWO important numbers in sampling: how fast, and how much. Sample rate is how fast, and the sample depth (number of bits used) is how much. They are separate discussions.
SAMPLE RATE
This is simply how many samples you take per second. According to the theory, you need to sample at least twice as fast as your highest frequency. If your music has sound up to 20KHz, you need to sample at least 40 KHz. Now for the assumptions. First, you have NO frequency content in the signal above 20 KHz – not a bit. Second, when you play back the recorded signal, you need to block ALL output frequencies above 20KHz. If you do this, the output will be EXACTLY the same as the input. The devil is in the details. The big thing here is that there is no such thing as a perfect filter – either on the input side or on the output side. There is no such thing as a filter that can pass signals at 20,000Hz and block all signals at 20,001Hz. Not possible. To get around this, you need some safety margin. That is why CDs sample at around 44KHz – about 10% over that Nyquist says you need. This is to give the filters some wiggle room. You can start to block at 20KHz, by the time the frequency gets to 22KHz, the filter has had time to kick in.
Now, if you have music up to 20KHz, and you sample at 96KHz, that gives you a LOT of wiggle room for the filters. It would be hard to design a filter that could NOT eliminate all frequencies above 48KHz if it could start at 20KHz. This means that your filters can do a far better job and you do not have to worry at all about aliasing (what happens if you break Nyquist’s rule)
Now, if you look at a reconstructed signal WITHOUT the filter, you will see a “stair-step” pattern. Check out the “DAC Output” graph here:
http://www.ni.com/white-paper/5535/en/
What you are ACTUALLY seeing is the original signal with some high-frequency harmonics. If you use a good enough filter, you can almost completely eliminate those “stair step.” With perfect filters, the output matches exactly the input.
Sample Depth
An ADC and a DAC have a finite number of bits. When you sample a signal, you grab the input at a particular moment in time. When you grab, you have to turn it into a number. How many numbers do you need? CD standardized on 16 bits. That means that you get a number between 0 and 65,535. If the actual voltage corresponds to 200.2356, it gets rounded to 200, giving you an error of 0.12%. The lost 0.2356 is the quantization error. If you use more bits, you throw away less. 24 bits (current standard for ultimate quality in the studio) uses numbers between 0 and 16,777,215. Scaling our input up to cover the new range, our new input is 51,260.3136. We throw away the .3136 so the error is 0.0006%. Each extra bit added will cut your error in half. Since we added 8 bits, our new error is 1/256 what our old error is. If you get your error low enough, it will be so small that you cannot hear it.
PUTTING THEM TOGETHER
So, when you sample, you can get errors from sampling (quantization errors) and also errors from inadequate filters. The more bits, the less quantization error you get. The higher you sample, the easier it is to get the filters to do a good job.
So, in theory, if you sample fast enough, and with a good enough filter, and use enough bits, the samples signal should be indistinguishable from the original.