Audio signal is an analog signal. Physics describe it as a wave. Analog signal cannot be perfectly recreated using digital processing. Such process can be seen as an attempt to store Pi number using floating-point arithmetics. Using higher storage precession (decimal places) we can achieve values closer to the original, but each additional digit has lower weight (value). Ultimately, no matter how high precision we use, we can never perfectly recreate the original value.
The same principle applies to digital processing of analog signals. Digital signal must be stored using limited number of bits and thus values it can store as limited. Analog signal is a continuous set of values. Digital recreation of analog signals is conducted using a sampling process. Sampling is nothing more that saving sequence of samples to created a discrete-time signal. Sampling is done by measuring values of continuous signal at so called sampling frequency. CD audio uses sampling frequency of 44,1 kHz, that is 44100 samples are taken in one second.
Quality of digital signal is measured in bits of information per sample. Audio is typically recorded at 16-bit depth. Bit depth informs about sample resolution. The higher the bit depth, the better the sampling and signal quality. Value mapping process must ensure that values can fit a 16-bit set of values. The process of mapping analog values from larger set to output values in a smaller set, and the information lost in the process is referred to as quantization noise.