The rule of thirds is a technique that was developed long before photography was invented and is still used today in other visual arts, like painting.
It's a basic skill for improving the composition of your pictures. And a thoughtful composition is the main difference between amateur snapshots and professional-quality photographs.
Imagine a grid of four lines, two horizontal and two vertical, that divides the picture plane into thirds [source: Stephenson]. You end up with nine equal sections. Try to place your main subject at one of the four spots where the lines intersect. That means not in the middle and a bit higher or lower than center.
When shooting a landscape, put the horizon at one of the horizontal lines. Use the upper one if you want to emphasize the foreground. Place the horizon at the lower line to make the background more prominent. Align buildings or other straight objects with one of the vertical lines [source: Photographymad].
You need to be aware of the rule of thirds, not obsess over it. Sometimes breaking the rule will give you a great picture, too [source: Rowse]. But knowing the principle lets you analyze pictures and see how they could be improved.