The above poster made good points, I would like to add an example:
An audio signal is continuous. A digital signal isnt - its chopped up. The number of chops, and their accuracy is dictated by sample rate and bit depth. For example:
A 16 bit bit-depth will give you 2^16 = 65536 'levels' that your audio signal is divided into. The signal is 'quantised' into these levels. Lets call this peice of info a sample.
The number of times a sample is played a second is the sample rate. I.e. every second 44,100 samples are taken when a sample rate of 44.1k is used. The human ears freq range is 20Hz to 20kHz. To accurately sample a 20kHz signal in the digital world, it must be sampled with a rate of 40kHz due to 'Nyquist', otherwise you get nasty freqencies appearing in the low end of your audio signal. Its the same concept as to why car tyres appear to be rotating in reverse.
Thats it all very simply.