A theorem stating that when an analogue waveform is digitised, only the frequencies in the waveform below half the sampling frequency will be recorded. In order to reconstruct (interpolate) a signal from a sequence of samples, sufficient samples must be recorded to capture the peaks and troughs of the original waveform. If a waveform is sampled at less than twice its frequency the reconstructed waveform will effectively contribute only noise. This phenomenon is called "aliasing" (the high frequencies are "under an alias").
This is why the best digital audio is sampled at 44,000 Hz - twice the average upper limit of human hearing.
The Nyquist Theorem is not specific to digitised signals (represented by discrete amplitude levels) but applies to any sampled signal (represented by discrete time values), not just sound.