The Nyquist rate is the theoretical minimum that allows you to distinguish one frequency from another. Sampling a higher frequency will cause an alias component to appear. This means that in practice, there must be analog band-limiting before the signal is sampled to reject any out of band signals before they are aliased to an in-band frequency and cannot be removed. The closer the band limiting cutoff comes to the nyquist frequency the more extreme the roll-off requirements for this band-limiting. Oversampling relaxes the band-limiting requirements, and can also increase the bit depth at lower sample rates. See PDM microphones for an example where this is taken to the extreme.