In digital audio, the term is used to define the number of bits a digital device uses to process audio. While sampling frequency determines the outer frequency limits that a piece of hardware is capable of processing, bit depth refers to the dynamic range that can be captured during recording. The number of possible "levels" that can be recorded at 16-bit is 65,536, while this figure jumps to 16,777,216 using 24-bit hardware. The human ear is very sensitive to these levels, and given properly implemented converter designs, 24-bit recordings will sound more "open" than 16-bit recordings. However, it is also true that a top of the line 16-bit converter could sound better than a very poorly implemented 24-bit converter. Although bits and sampling frequencies are important specifications, the kinds of filters used, and the integrity of the audio path prior to the converters is also very important as to how a particular converter will sound.
(See Floating Point)