Is basically a simplification of the Golden rule.
About rule
The rule of thirds, when applied to photography and graphic art, makes the image more interesting to the eye.

Why is the rule so effective?
Using the rule of thirds draws the viewers eye into the composition, instead of just glancing at the center. By placing the subject off center, you also embrace more blank space.

The rule of thirds is also helpful for highlighting an interesting background.

Why is the rule so useful?
Balance
Dynamism
First, by positioning key elements at rule of thirds intersections or gridlines, your photo becomes balanced. this looks great and feels right to the viewer.

Example mine iphone camera always active in rule of thirds mode.
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