A contour is a three dimensional form, a modulation of the surface a topographical (define) feature. Visually, we percieve contours in three ways; naturally using our stereoscopic vision, noticing color changes due to shading and detecting edges. Stereoscopic vision is used by creatures whose two eyes provide overlapping visual fields. Each eye presents the brain with an image within which the comparative displacement of objects is directly related to their distance from the creature.

DO THIS:(30 seconds)
Shut one eye. Place the image of your thumb over the image of a distant thing. Shut that eye and open your other eye. Notice that the image of your thumb no longers conceals the distant thing. Notice the closer your thumb is to your eye, the more your thumb appears to "jump" over in the visual field.
The brain combines the two images into one, using the displacemnent to produce a "feeling" of depth.
 

DO THIS:(3 seconds)
Catch a thrown object with only one eye open.

A drawing, painting or traditional photograph is a single image. Although it is viewed with two eyes, both eyes see the same image. No stereoscopic feeling of depth is present. Its image, no matter how realistic, will always have this essential flatness. The second method of contour perception relies on the phenomena of light. As light illuminates a surface's area, it bounces off and some of it enters our eyes. If less light illuminates a given area, less bounces off, and less light enters our eye. Illumination is strongest when the light's direction is perpendicular to the surface. Less light illuminates a given area if the surface is at some other angle. And, of course, illumination drops greatly when the surface is turn so that the surface is in shadow. Artists commonly call this "shading."
Illusions of shading may be produced by coloring, especially light and dark (value) and are commonly used to create the appearance of contours and depth in artworks. The third method of seeing form involves edge detection. For our purposes, there are two types of edges. One type, we call "primary" edges are seen when the shape and viewpoint conspire to create a horizon, in other words when the shape disappears behind itself or, in some other way, ends.
The other type, secondary edges, are boundaries that mark a more or less abrupt change of direction of a surface, such as the near edge of a cube seen from a 45 degree view (kitty corner).

Contour Edges.
A contour may end by disappearing behind another contour (of itself or something else) the way the edge of your fingernail vanishes under the flesh of your finger or vice versa. Or the way the edge of a finger may disappear under a ring.
A contour may end because the modulation of the surface diminished to the point where there is longer any horizon (define). If you hold your finger in front of your face and point it at your right ear, you will observe that the bottom contour of your index finger disappears to the left in this manner.
Some objects have contours that have no terminus. An egg's contour is continous, with no beginning or end. In the case of an egg an artist would have to start at an arbitrary point.