Nyquist's theorem is one of the most fundamental in digital signal processing. It says that when sampling a signal, the sample rate needs to be at least twice the highest frequency which appears in the signal. Sampling at this rate ensures that the signal can be reconstructed perfectly from the digital samples.

A simple example: most humans can't hear sounds above 20kHz. Thus, when sampling audio data, 40000 samples per second are sufficient to ensure that no audible sound is lost. Compact discs use 44000 for good measure.