The rule of thirds says that objects should be placed a third of the way from the top or bottom of the frame, or a third of the way in from the sides, rather than in the centre of the frame.
Imagine horizontal and vertical lines splitting the image up into thirds; some cameras and image-editing programs can display a grid which does this. In this picture, the horizon's been placed on the bottom 'third', while the silhouetted figure's positioned on the left 'third'.
It's true that the rule of thirds can often improve a composition, but it's no guarantee of a good picture on its own. It's worth doing if no better compositional arrangement suggests itself, but it doesn't provide much compositional strength of its own.
If you look at any picture which demonstrates the rule of thirds, you'll find it's either very dull, or has some other compositional element that's actually much stronger.
This picture appears to demonstrate the rule of thirds very well, but impact the compositional impact actually comes from the framing effect of the clouds, the tones, and the direction of the figure's gaze. These are related to two more compositional tools - shapes and lines - which have a much more powerful effect. If you can harness these, the rule of thirds becomes rather irrelevant.
Basically, if the rule of thirds is all you've got, you're in trouble.
