In music dynamic range would most often refer to the range of smallest to largest value of volume.
Consider, for example, the dynamic range of human sound perception. The difference between a loud concert and a quiet whisper could be 100 dB, which is about (100 / 10)^10 = 10,000,000,000 (a concert is about 10,000,000,000 louder than a whisper). The dynamic range of the human ear is probably larger, even though at some point speech recognition is probably lost.
The dynamic range of digital audio is directly related to its sampling resolution. 16-bit audio (such as audio CDs) can have a ratio of loudest to quietest sound of 2^15:1, which is equal to about 20 log10(2^15:1) = 90 dB. In other words, the dynamic range of 16-bit audio is approximately the same as the dynamic range of human hearing.