A theory developed by mathematician Harry Nyquist in the 1920s, which states that (among other things), for a digital conversion of an analog signal, the highest signal frequency that can be properly represented in the digital data is 1/2 of the sampling rate. The specific implication for electronic music is that a sampler or digital synthesizer must record or process the individual digital words at a rate at least twice the highest frequency present, or desired to be present, in the converted analog signal. If higher frequencies are present in the signal being sampled or computed, they must be filtered out, or else aliasing will result.
In a practical system, some form of low pass filtering is usually necessary to eliminate frequencies above the Nyquist rate. And because no filter is capable of an infinite slope, some latitude has to be allowed between the highest desired signal frequency and the Nyquist rate. Thus, the common Compact Disk recording rate of 44.1 kilo-samples per second (incorrectly but frequently written as 44.1 KHz) has a Nyquist rate of 22.05 KHz, whereas the generally accepted upper limit of human hearing is 20 KHz; the extra range allows for the anti-aliasing filter to roll off. Some early samplers recorded at rates as low as 10 kilo-samples/second, limiting the usable audio bandwidth rather severely, which is one factor accounting for the low-fi sound of those instruments. However, newer samplers, digital synths, and professional digital audio equipment usually record at a rate higher than the Compact Disk rate so the anti-aliasing filters can be of less drastic design. (Filters with very steep slope are noted for having undesirable phase shifting characteristics.) 48 or 50 kilo-samples/sec is pretty common in newer gear, and some equipment may be capable of much higher; rates of up to 188 kilo-samples/sec are available in a lot of recent pro audio gear.