A key factor at play is how the eye naturally tends to read a web page, or a photo, or a painting... or actually every single scene of life we visually experience(!). The Rule of Thirds is a principle that describes how this manifests itself: our eyes tend to go to four specific locations when they scan a scene, these locations being the inner intersection points of a 3x3 grid overlaying the scene.
Carrie Cousins has several blog posts on this (Using the Rule of Thirds as a Grid Outline, Understanding the Rule of Thirds in Web Design) that particularly resonated with me. Here is one of her images I found particularly useful:
|Where Our Eyes Focus on a Scene (from Carrie Cousins, Using the Rule of Thirds as a Grid Outline)|
"You can work with or against the rule of thirds, but you can’t eliminate it."