A digital audio signal is defined by these two parameters – the sample rate is essentially how many times per second a digital converter takes a “snapshot” of your audio – a 44.1khz signal means that 44100 times in a second, a section of the incoming or outgoing signal is converted.  The bit depth is the detail of that snapshot, represented by a binary value of the size specified by the bit depth: a 16-bit audio sample is represented by a number between -32,768 and +32,768.  A 24-bit signal is +-8,388,608.

Okay, great.  So what does that mean, really?

The sampling rate defines the frequency that can be reproduced – the “Nyquist frequency” is one-half the sampling rate, so the maximum frequency a CD can reproduce is 22khz, or about 2khz higher than humans can hear (at the best of times, most of us top off at around 17khz).  Bit depth is the resolution, and subsequently the “detail.”  Higher bit depths mean higher possible dynamic ranges, lower noise floors, etc.