An anti-aliasing filter is commonly used in conjuction with digital signal processing and is a filter to restrict the bandwidth to approximately satisfy the Shannon-Nyquist sampling theorem. Since the theorem states that the power of frequencies outside the bandwidth must be zero then the anti-aliasing filter would have to be a perfect filter to completely satisfy the theorem. This is true because a bandwidth-limited filter must have infinite time to filter. So every realizable anti-aliasing filter will permit some aliasing to occur. The amount of aliasing that does occur depends on how good the filter is and what the sampling rate is.
The purpose in oversampling is to relax the requirements on the anti-aliasing filter or to further reduce the aliasing. Since anti-aliasing filters are analog, oversampling allows for the filter to be cheaper because the requirements are not as stringent.
Frequency spectrum shape
Most often, an anti-aliasing filter is a low-pass filter. However, this is not a requirement. The Shannon-Nyquist sampling theorem states that the sampling rate must be greater than twice the bandwidth, not maximum frequency, of the signal. For the types of signals that are bandwidth limited, but not centered at zero, a band-pass filter would be used as an anti-aliasing filter. For example, this could be done with a single-sideband modulated or frequency modulated signal. If you desired to sample channel 200 (in the USA) of an FM radio broadcast, then an appropriate anti-alias filter would be centered on 87.9 MHz and 200 kHz bandwidth (or pass-band of 87.8 MHz to 88.0 MHz) and the sampling rate would be no less than 400 kHz.
See also
