One of the age-old and most popular principles of composition in photography is called the rule of thirds. By understanding and applying this rule in your own photography, you'll begin to produce more effective, well-balanced, exciting and dramatic pictures, pictures that more naturally engage the viewer's eye.
When applying the rule of thirds you take the main subject/area of interest you're working with and use the rule to position the subject in the image space. For instance, perhaps you are taking a still life picture of a flower in a vase, against a plain background. The flower itself would largely be the main subject/area of interest – it would be potentially what the viewer would be most drawn to. With the rule of thirds you'd take the flower and position it in the image space according to the rule, and this helps to produce a more naturally appealing picture.
So what is the rule of thirds?
The rule of thirds itself divides the photographic image into nine equally spaced segments. Two horizontal lines at an equal distance go across the image, and two vertical lines spaced at an equal distance go down the image - these lines produce the nine segments. Where these horizontal and vertical lines cross are called the intersection points. There are four intersection points in total, and these points are the fundamentals we work with in the rule of thirds - the rule is simply positioning the main subject of interest onto one of the intersection points!
Let's go back and apply the rule of thirds to the example of photographing the flower in the vase. With the rule we have a number of options for placing the flower in a vase in a composition, and one aim can be with helping to purposely draw the eye to the flower itself. Here to do this we use one of the four intersection points and place the flower onto/or very near to one of these points. That's it! Now we have positioned the flower according to the rule of thirds. By placing a subject in this way it really helps to engage the viewer's attention onto the actual flower, and producing an overall more appealing composition.
So here we've seen the principles of the rule of thirds applied to a subject matter. With the rule of thirds is simply that you position the main subject off from the centre of the image onto one of the four intersecting points. Decide on the main area/subject of interest for your photographs and begin exploring with the rule by positioning the subject onto different intersecting points. Using this rule as a good basis for your photography, you'll be able to really enhance your compositions, and add greater impact in your pictures.