When sound is represented digitally the amplitude of the sound wave is taken at different points in time and recorded as a number. How often a sample is taken defines the sampling rate. What number is used to record the amplitude of each sample defines the sampling resolution. In 8-bit recording, for example, each sample is represented by an 8-bit number. Eight bits can only represent 256 numbers (2 to the power of 8) and so only 256 different amplitudes can be written. This makes for a very small dynamic range of a sound recording. A 16-bit recording uses 16 bits for each sample. 16 bits can represent 65,536 different numbers and amplitudes, which makes for a much better dynamic range.
The sampling resolution is the representation (or size of the numbers) used to write samples in digital sound recording.
The sampling resolutions used regularly in current digital music practice are: 8-bit, 16-bit, 24-bit, and 32-bit. 8-bit digital sound uses only positive (unsigned) integer numbers by convention, but not always. 16-bit and 24-bit digital sound usually uses positive and negative (signed) integer numbers. 32-bit sound is rare and usually uses signed floating point numbers between -1 and 1. 16 bits are used in contemporary CD audio.
The selection of the 16-bit sampling resolution used in CD audio was not chosen at random. 16 bits can properly represent dynamic ranges of about 90 dB, which is basically the maximum dynamic range of human hearing.
The advantages and disadvantages of larger and smaller sampling resolutions are obvious. Larger sampling resolutions allow for larger dynamic ranges, but require more recording space.