What is Nyquist frequency (rate)? When is this important?

The Nyquist–Shannon sampling theorem states that to represent a signal without loss of information, you must sample at a rate of at least twice the highest frequency component present in the signal. That minimum rate (2 × f_max) is the Nyquist rate, and half the sampling rate is the Nyquist frequency.

If a signal contains energy above the Nyquist frequency, those components fold back ("alias") into the sampled band as false lower-frequency content that cannot be removed afterward. This matters anywhere a continuous signal is digitized or reconstructed:

• ADC/DAC and data acquisition: choosing an adequate sample rate for the signal bandwidth of interest.
• Anti-alias filtering: a low-pass filter before the ADC must attenuate everything above the Nyquist frequency so it cannot alias.
• DSP, audio, communications, and control systems: ensuring sample rates and reconstruction filters preserve the signals of interest. In practice designers sample comfortably above 2× and use practical (non-ideal) filters to leave guard band.