The rules of thirds says that you should line up the main subject of your photo along one of the off-center grid lines
instead of centering it.

Some cameras have a digital grid you can enable on the viewfinder to see these lines. You can also use this technique by cropping a photo after it is taken to follow this rule.

These are examples of the rule of thirds.

This photo is shown on the left as originally taken (not following the rule of thirds), and then on the right cropped to follow the rule.

Here is more information on the rule of thirds:

• “Rule of Thirds” on Wikipedia
• “Rule of Thirds” from Digital Photography School
• “How to Use Photography’s Rule of Thirds – And When to Break It” from Digital Trends