The Nyquist frequency, named after Harry Nyquist by Claude Elwood, is the half of the sampling frequency of a signal.
The Nyquist-Shannon sampling theoremEdit
The Nyquist-Shannon sampling theorem states that for a signel to be reconstructed the highest frequency in the signal has to be lower than the half of the sampling frequency, the Nyquist frequency. Vice versa it means that the sampling frequency must be as twice as high as the highest frequency in the signal. If this criteria is not given, artifacts, known as Aliasing, will appear.
Assuming we have a sine-wave with the frequency 0.5Hz and a sample frequency of 0.5Hz, starting to sample at 0 seconds, the sampled values will always be 0. If the sampling frequency is just a bit bigger, the sampled values wouldn't be only 0, but wouldn't represent the original sine-wave at all, which would make reconstruction impossible too.