The Golden Ratio is like the Rule of Thirds but on steroids. By putting a curved line, rather than a straight line across the page, the viewer's eyes are drawn around the picture.  As you go around the spiral, you end up at the tight coil where your point of interest is.

Some 20th Century artists and architects, including Le Corbusier and Dali, have proportioned their work to adopt the Golden Ratio. But it isn't just man-made, as the Golden Ratio appears in some patterns of nature: see below.

This is just a cool idea to have in mind while taking photos. It is a bit complex, but if you just think about while you're with your camera, then you're doing the job.