When an analog signal is converted to digital, it is represented in the digital form by a series of binary numbers, each of which represents the signal value in a point of time. The number of binary digits, or bits, in each word is known as the bit width. As in the case with decimal numbers, the more bits, the more precisely the binary numbers can represent the signal.
So, the bit width determines the noise floor for the digital signal. Very roughly, each bit adds 5 dB to the signal-to-noise ratio. If the output of a digital signal is turned up louder than the signal-to-noise ratio, distortion will be heard. Early samplers, such as the Fairlight CMI, used 8 bit binary numbers. This gave a S/N ratio of only about 40 dB, which accounts for the "crunchiness" of these early samplers. Music CDs use a bit width of 16 bits, or about 80 dB, which is more than the available dynamic range in a moderately quiet room. (Figuring that a moderately quiet room will average about 60 dB sound pressure level, and the threshold of pain is at about 110 dB.) Modern samplers and the latest computer audio interfaces use bit widths of 20 or 24 bits.
The effect known as bit crushing adds distortion to signals by converting them to digital format and then chopping off the low-order bits to reduce the bit width.