A digital recording of a sound contains numbers that represent the amplitude of a sound at different points in time. Time is continuous and contains infinitely many points. Thus, the amplitude of a sound cannot be recorded for each point in time. It must therefore be sampled.
The sampling rate, also called "sampling frequency", is the rate at which sound is sampled and is usually represented as the number of samples taken in a certain period of time.
For example, a sample rate of 44,100 Hz means that the sound is sampled 44,100 times in each second and the digital recording of the sound contains one value for the amplitude of each channel for every 1/44,100 portion of the second.
Common sampling rates include 22,050 Hz, 32,000 Hz, 44,100 Hz, 48,000 Hz and 96,000 Hz. The sampling rate in an audio CD is 44,000 Hz (or 44.1 KHz). Higher sampling rates provide better sound quality, but require more space for the digital recording. According to the Nyquist-Shannon-Kotelnikov sampling theorem, the sampling rate can only properly represent sound with frequencies up to half of the sampling rate. Thus, a CD can only properly represent sound up to 22,050 Hz. The CD sampling rate is used as 20-22 KHz is considered the upper limit of the human ear. Contemporary digital recording equipment sometimes uses higher sampling rates. The disadvantage of higher sampling rates is: Higher rates use more space. The benefits are not as clear. It is possible that even though the human ear cannot hear frequencies above 20 KHz, it may be able to perceive distortions that higher frequencies have on audible sound. It is also possible that higher frequencies allow for better signal processing with smaller losses in quality (through equalizers, reverbs, etc.).