"Stacking the Composition" is a technique, often used by photojournalists and by wedding photographers who take a photojournalistic approach to their subject, in which one or more secondary subjects are placed strategically within the photograph, usually at a different plane.
These secondary subjects can provide a context for, a contrast to, or enhancement for the main subject of the photo.
Add context: The signs in the foreground are the subject, but the ferris wheel in the background tells us we're in an amusement park.
Stacking the composition requires good depth of field (a wide-angle lens is a good idea) and an organized visual sense, or else you run the risk of turning a photo into a distraction-filled mess. The best way to approach this technique is to look at a scene and ask yourself, "what in the background (or foreground) can make this a better picture?"
A complementary element: I posed the soldiers, but when the woman appeared in the doorway I shifted position to include her, quickly adding a secondary subject at a more distant plane.
A few examples? A little boy with his hand in the cookie jar is a good picture, uut his mom in the background catching him in the act is better. His sister behind her mom enjoying his brother in trouble is better still. This is a classic (although obviously set-up) way to stack the composition. The real challenge? Stacking the composition when you have no control over the scene.
Add depth: While the umbrellas comprise the main subject, the abandoned beach concession area has several secondary subjects on several planes. See the seagull on the roof? That's yet another sub-subject! Photos by Mason Resnick; Camera, Canon 30D, 18-55mm kit lens.