The Importance of Composition and Perspective
Compositions appear everywhere. In fact, anything you look at during every second you are awake can be considered a composition. As a photographer, what you need to do is be able to alter your perspective to create a composition not normally seen every day. The type of lens you are using may already help you achieve this. A wide angle lens, for example, will exaggerate the depth of an image far more than what you see in real life. A telephoto lens will make things look flatter (this is useful in portrait photography). One way you can easily achieve a different view is by crouching down to take shots from a lower perspective, or standing on something taller to take a shot from a higher perspective.
The 'rule of thirds' in photography states that your subject should be positioned 1/3rd of the way into the frame, and never dead-center. Your eyes are used to seeing everything you focus on, dead-center from your point of view. A photo with the subject off-center gives a more "relaxing" composition as it does not make the center of focus (the photo frame) within another center of focus (your viewing frame). The rule of thirds is there because it shows you a composition that can not be seen in real life. Go on, try looking at something in the room. Now move your head but at the same time, keep your eyes pointing straight forwards. Can you get what you were looking at before in focus now that it is not positioned dead-center in your frame of vision?
Keep in mind, however, that this "rule" should be considered more of a guide as sometimes you might want the dead-centered effect.