The purpose of these lines is to provide a guideline of where to place the main subject of your image. The main subject should be placed at a point where the lines intersect, or on one of the lines.
Many cameras have a feature that allows you to view gridlines through your viewfinder. Using this will help you place your subject according to the rule of thirds before you even take your shot!
Below is an example of an image taken using the rule of thirds.
