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

Flow effects in MRI produce a range of artifacts, e.g. intravascular signal void by time of flight effects; turbulent dephasing and first echo dephasing, caused by flowing blood.
Through movement of the hydrogen nuclei (e.g. blood flow), there is a location change between the time these nuclei experience a radio frequency pulse and the time the emitted signal is received (because the repetition time is asynchronous with the pulsatile flow).
The blood flow occasionally produces intravascular high signal intensities due to flow related enhancement, even echo rephasing and diastolic pseudogating. The pulsatile laminar flow within vessels often produces a complex multilayered band that usually propagates outside the head in the phase encoded direction. Blood flow artifacts should be considered as a special subgroup of motion artifacts.

Artifacts can be reduced by reduction of phase shifts with flow compensation (gradient moment nulling), suppression of the blood signal with saturation pulses parallel to the slices, synchronization of the imaging sequence with the heart cycle (cardiac triggering) or can be flipped 90° by swapping the phase//frequency encoding directions.

See also Flow Related Enhancement and Flow Effects.