Oversampling is the increase in data to avoid aliasing and wrap around artifacts. Aliasing is the incorrectly mapping of tissue signal from outside the FOV to a location inside the FOV. This is caused by the fact, that the acquired k-space frequency data is not sampled density enough.
Oversampling in frequency direction, done by increasing the sampling frequency, prevents this aliasing artifact. The proper frequency based on the sampling theorem (Shannon sampling theorem/Nyquist sampling theorem) must be at least twice the frequency of each frequency component in the incoming signal. All frequency components above this limit will be aliased to frequencies between zero and half of the sampling frequency and combined with the proper signal information, which creates the artifact. Oversampling creates a larger field of view, more data needs to be stored and processed, but this is for modern MRI systems not a real problem. Oversampling in phase direction (no phase wrap), to eliminate wrap around artifacts, by increasing the number of phase encoding steps, results in longer scan/processing times.

If the receiving RF coil is sensitive to tissue signal arising from outside the desired FOV, this undesired signal may be incorrectly mapped to a location within the image, a phenomenon known as aliasing. This is a consequence of the acquired k-space frequencies not being sampled densely enough, whereby portions of the object outside of the desired FOV get mapped to an incorrect location inside the FOV. The sampling frequency should be at least twice the frequency being sampled. The maximum measurable frequency is therefore equal to half the sampling frequency. This is the so-called Nyquist limit. When the frequency is higher than the Nyquist limit, aliasing occurs.
A similar problem occurs in the phase encoding direction, where the phases of signal-bearing tissues outside of the FOV in the y-direction are a replication of the phases that are encoded within the FOV. This signal will be mapped, or wrapped back into the image at incorrect locations, and is seen as artifact.

See also Aliasing Artifact.

Quick Overview
Please note that there are different common names for this artifact.

Backfolding always occurs due to wrong phase encoding caused by objects outside the planned FOV. Phase encoding gradients are scaled for the field of view only. Tissues outside the FOV do not get properly phase encoded relative to their actual position and 'wraps' into the opposite side of the image. The Backfolding artifact projects image contents which fall outside the imaging FOV back into the image; the back folded information thus reappearing on the other side of the image. In fact, information along the phase encoding direction can be viewed as projected onto a cylindrical screen with a circumference corresponding to the linear field of view dimension in the phase encoding direction.

See also Aliasing Artifact.