For a band-limited continuous-time signal, the Nyquist-Shannon sampling theorem states when ideal reconstruction from uniformly spaced samples is possible.

If the signal contains no frequency component at or above $B$, then ideal reconstruction is possible when

$$f_s>2B.$$

The threshold $2B$ is the Nyquist rate for that band limit. Equivalently, for a fixed sampling frequency $f_s$, the frequency $f_s/2$ is the Nyquist frequency.

The frequency-domain explanation comes from sampling's effect on the spectrum: uniform sampling produces repeated spectral copies separated by $f_s$. When $f_s>2B$, neighboring copies remain separated; when they overlap, different original frequencies become aliases and cannot be distinguished from the samples alone.

Real signals are rarely perfectly band-limited. Measurement systems therefore commonly use an anti-alias filter before sampling to attenuate frequencies above the range the sampler can preserve.

The theorem is a reconstruction result under explicit assumptions, not a claim that any waveform is preserved whenever the sampling rate merely seems high.