To understand this rule you must split your frame into threes, by drawing three horizontal line and three vertical lines. If you place your main objects on the lines of the where the three lines cross it will give more dramatic to your picture. This article I read said "It will allow your viewers eye to sit comfortably there instead of fight against a center placed element" (Photography). It makes your picture feel more natural and lets your point of view get across to the viewer. Another rule is when taking a picture of landscape and the horizon is in the picture, it should always be up toward the top line to make it feel more real. The rule of thirds help your picture seem much more natural to a viewer when presenting it.
"Photography Composition: Rule of Thirds." Icon Photography School, n. d. Web. 7 Sep. 2011.