Motion of material being imaged, particularly flowing blood, can result in many possible effects in the images.
Fast moving blood produces flow voids, blood flowing in to the outer slices of an imaging volume produces high signals (flow related enhancement, entry slice phenomenon), pulsatile flow creates ghost images of the vessel extending across the image in the phase encoding direction (image misregistration).
Flow-related dephasing occurring when spin isochromats are moving with different velocities in an external gradient field G so that they acquire different phases. When these phases vary by more then 180° within a voxel, substantial spin dephasing results leading to considerable intravascular signal loss.
These effects can be understood as caused by time of flight effects (washout or washin due to motion of nuclei between two consecutive spatially selective RF excitations, repeated in times on the order of, or shorter than the relaxation times of blood) or phase shifts (delay between phase encoding and frequency encoding) that can be acquired by excited spins moving along magnetic field gradients.
The inconsistency of the signal resulting from pulsatile flow can lead to artifacts in the image. The flow effects can also be exploited for MR angiography or flow measurements.

See also Flow Artifact.

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.

The occurrence of a low signal in regions of flow. For a spin echo sequence, this is caused in part by a lack of refocusing of blood, which is excited by the 90° pulse but not by the 180° pulse. For a gradient echo sequence, this is caused by the dephasing of blood signal.