Dynamic range in audio is the difference between the system noise floor and the maximum undistorted signal. The noise floor defines the smallest usable level, as the signal needs to be distinguishable from the electronic background noise. On the other end of the range it is important that the signal remains undistorted, because it is possible to push the signal above the limits of the system at the cost of clipping it, which introduces distortion meaning the signal integrity is lost. Human hearing has a dynamic range of about 140 dB (starting from about -9 dB SPL due to human varying frequency sensitivity), but high levels cause permanent hearing damage and are not advisable.
Dynamic range can be expressed in decibels, but also in bits, especially in digital audio. Each bit doubles the signal that can be represented, and thus the dynamic range. Thus each bit is equivalent to 20*lo g 10 ( 2 ) ≈ 6.02dB
Therefore a 16 bit system has a dynamic range of 96 dB (16*6), and a 24 bit system a theoretical dynamic range of 144 dB. I'm saying theoretical because I have never encountered a converted, either digital-to-analog or analog-to-digital that could fully utilise that range. The absolute best I've seen have been 22-23 bits at maximum. The situation is further confused by the THD+N (Total Harmonic Distortion + Noise) value, which states the undistorted range above the noise floor. This value is generally lower than the dynamic range reported by the manufacturer. There are subtle differences and the different specifications have different uses, but it most cases it's best for a user to look at the worst-case values.
In music the situation is a bit different. There the dynamic range is the difference between the loudest and quietest portions of a song or album (or playlist etc.). Unfortunately louder is generally perceived as better, which led to the so called loudness wars in the late 1990s, and the effects are still visible. In order to make their music louder than others, the engineers began compressing the dynamics and pushing the loudness, sometimes until the point of clipping. This has fortunately become less of a problem with streaming services limiting the maximum loudness of songs.
Barring such exceptions as the 1812 Overture with it's cannons, classical orchestral music can have about 80 dB of dynamic range. Human speech tends to about 40 dB dynamic range. Some of the worst offenders from the loudness wars have less than 6 dB dynamic range! Based on this, we can pretty confidently say that the 16 bits made commonplace by CD is enough for most applications.