Aliasing
Aliasing, or wrap-around, can occur whenever any part of the object to be imaged extends outside the imaging volume (FOV). Anatomy that exists outside the FOV is mapped inside the FOV, on the opposite side of the image. Anatomy outside the FOV still produces a signal if it is in close proximity to the receiver coil.
Aliasing on a head image (phase encoding left-right).
Consider this diagram (phase encoding up-down):
The anatomy at the top of the body in this diagram extends beyond the field-of-view in the phase encoding direction. This anatomy will be encoded with a rate-of-change of phase of, say, +185° over the many phase encoding steps. But this is indistinguishable from the rate of change of phase of -175° over the many phase encoding steps, and signal will be mapped to the "-175°" location.
Although this phenomenon may occur in the frequency-encode direction, it is generally more often seen along the phase encode axis. This is because aliasing in the frequency-encode direction can be remedied by applying a low pass filter on the demodulated signal, or over-sampling in the frequency encode direction, for which there is no time penalty. Phase however is circular—a 370° angle is indistinguishable from a 10° angle. There is no simple way to filter phase as is possible with frequency. One can over-sample but this incurs a time penalty (more phase encoding steps). The problem of aliasing is solved with a number of techniques.
Further reading on this topic:
Books: MRI From Picture to Proton p48-49, 96-98, 129, MRI The Basics p175-177, Q&A in MRI p133-141
Online: Basics of MRI, MRItutor, St Paul's 1, 2, e-MRI 1, 2