The rule of thirds is one of the main rules when it comes to photography. It comes from the theory that the human eye naturally gravitates to certain points in an image. It is actually the most known rule of photography.
With the rule of thirds, photographs are divided with two imaginary lines horizontally and two vertically, splitting it into three rows, three columns and nice sections.
Important elements of the photograph should be placed on or near the imaginary lines on the image.
With landscapes, it is better if the horizon falls on the top imaginary line or the bottom imaginary line as opposed to directly in the centre (which is natural)
With portraits, it is best if the eyes are located where the horizontal and the vertical lines intersect.