The Rule of Thirds is one of the most popular 'rules' used by photographers and artists. The basic principle behind the rule of thirds is to mentally divide up the 'view' on your camera into 9 segments by vertically and horizontally breaking the view into thirds.
The four 'corners' of the middle segment would be where you would place your subject or point of interest. Another effective way of using this rule is to 'take up' two thirds of your photo with the subject so that they are against a background, and this makes the subject stand out.
