The basic idea is how many discrete points are required before we can't distinguish discrete points any more and it looks (or sounds) continuous.

The basic limit of human hearing is generally quoted as 20Khz (20,000 cycles per second).

To capture this you need (at least) twice as many samples per second (so you get at least 2 points per cycle)

This is the basic theory for pure sinusoidal sound waves.

More complicated wave shapes can be made up from superimposing lots and lots of sine waves.

While it is true that the standard ear can only distiguish upto 20Khz as a pure sine wave, there is some evidence that we can distiguish the change in waveform shape due to the overtones from higher frequencies.

This is (one reason) why some audiophiles still prefer the anolog vinyl records to digital CDs.

Have a look at this wikipedea page:

http://en.wikipedia.org/wiki/Aliasing