The “Rule of Thirds” is a visual rule on photos and art. If you take your photo and fold it in three equal parts in both directions what you end up with is two lines horizontaly and two vertical. These line are areas in the work that the eye find more dramatic. The place were the lines intersect are focal points. The eye find the four points most dramatic. When shooting photos or painting art keeping these points and site lines you can make better images than keeping everything centered.
The bride photographed in this is lined up with the left sight line. The eye focuse on her first then follows the blinds off the photo. Because subject is on the sight line the viewers eye stops on her. Had the photographer had her in the center of the photo the viewer could glance over the photo and not noticed what the subject was doing.
This one the Pier post is on the left sight line. Two things help make this more dramatic. One the placement of the pier on the sight line and increasd appiture with fast shutter reduced the depth of field which will be talked about later.
Since alot of works here are of flowers does it still work with them? Yes if you look at macros of flowers they are taken at a dramatic angle and they space the flower to touch the four focal points. The center of the flowers will be on the sight lines. The photo about was taken on a dramatic angle and the right flower is on the sight line.
The Butterfly no theres not going to be a world of doom that the butterfly effect. Insects photos work best with the macro eye on the focal points or spread the body bo be balanced inbewteen two sight lines.
Portraits are a little diferent in the rule. Two basic types of portraits use the thirds rule. The Standard Portrait which used the upper and lower sight lines to balance the hair line and the base of the neck. Look at just about every wedding portrait or school portrait. The side sight lines frame the sides of the face.
Type II portrait is the close up portrait. This portrait is The dramatic portrait type. The famous portrait of Winston Churchhill during WWII his eyes are on the upper two focal points and his chin with cigar was on the bottom sight line.
This is just a little bit into the use of the rule of thirds. I found some cameras will overlay a grid on the lcd screen. Panasonic cameras have this funtion. Look at your photos and see if the ones you like more have the dramatic fetures on the sight lines or focal points.
You can read a little more at wikipedia
The photo on wikipedia is a terible exsample of the rule. It brakes the 2/3 rule of sky and horizon. Which is for a perspective discustion