Shannon's Sampling Theorem states that a continuous signal can be completely represented by its samples if it is sampled at a rate greater than twice its highest frequency. This minimum rate is known as the Nyquist rate. If the sampling rate is too low, the original signal cannot be accurately reconstructed, leading to a phenomenon called aliasing. The theorem is fundamental in the fields of signal processing and communications, as it provides the basis for converting analog signals into digital form. By ensuring proper sampling rates, engineers can preserve the integrity of the information contained in the original signal.