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

Patient motion is the largest physiological effect that causes artifacts, often resulting from involuntary movements (e.g. respiration, cardiac motion and blood flow, eye movements and swallowing) and minor subject movements.
Movement of the object being imaged during the sequence results in inconsistencies in phase and amplitude, which lead to blurring and ghosting. The nature of the artifact depends on the timing of the motion with respect to the acquisition. Causes of motion artifacts can also be mechanical vibrations, cryogen boiling, large iron objects moving in the fringe field (e.g. an elevator), loose connections anywhere, pulse timing variations, as well as sample motion. These artifacts appear in the phase encoding direction, independent of the direction of the motion.

Motion artifacts can be flipped 90° by swapping the phase//frequency encoding directions.
The artifacts can be reduced by using breath holding, cardiac synchronization or respiratory compensation techniques: triggering, gating, retrospective triggering or phase encoding artifact reduction. Flow effects can be reduced by using gradient moment nulling of the first order of flow, gradient moment rephasing or flow compensation, depending of the MRI system.
Peristaltic motion can be reduced with the intravenous injection of an anti-spasmodic (e.g. Buscopan).
By using multiple averages, respiratory motion can be reduced in the same way that multiple averages increase the signal to noise ratio. Noticeable motion averaging is seen when four averages are obtained, six averages are often as good as respiratory compensation techniques and higher averages will continue to improve image quality.
In some cases will help a presaturation of the anatomy that was generating the motion.

See also Phase Encoded Motion Artifact.