An example is illustrated below, where the reconstructed signal built from data sampled at the Nyquist rate is way off from the original signal.
Under sampling causes frequency components that are higher than half of the sampling frequency to overlap with the lower frequency components. As a result, the higher frequency components roll into the resconstructed signal and cause distortion of the signal. This type of signal distortion is called aliasing.
The schematic below repeats the above aliasing argument in the frequency domain.
Spectrum of Sampled Signal
Sampled at less than the Nyquist rate