The bitdepth is an important but a bit a confusing concept since its use varies among audio formats. The "classical" meaning is applicable to PCM style encodings. When refering to mp3 or other lossy type formats and DSD type formats the bitdepth is not used in the same way. When referring to formats such as wav or aiff the bitdepth is crucial to the dynamic range that is "encoded" in the sound.
Common Audio Bit Depths
For a detailed explanation on bit rates and their importance have a look at this wikipedia article: http://en.wikipedia.org/wiki/Audio_bit_depth