A mathematical vector used to change the coordinates of a point (positional vector) in one coordinate system (CS) into that point's coordinates in a different CS that is translated but not rotated with repect to the first CS. The translation vector's coordinates are added directly to the points initial coordinates to yield the transformed coordinates of the final CS. See also Rotation Matrix and Homogeneous Transformation Matrix
For detail and illustrations see the tutorial:
REFERENCE COORDINATE
SYSTEMS AND TRANSFORMATIONS