When a point or line is selected along with a line or a Surface one of the displays is "closest distance". In the case of a point and a line, the closest distance is the length of the perpendicular from the line to the point (note the closest distance between the point and the line segment to the point without extending the line). In the case of a point and a Surface, the closest distance is the length of the perpendicular from the plane of the Surface to the point (for 3Point surfaces), while the closest distance between the point and the defined surface without extending the plane is also shown.
In the case of two lines or edges, the closest distance is the distance between the perpendicular between both lines (this will be where the lines are closest). If the two lines are on the same plane this closest distance will always be zero unless the lines are perfectly parallel.