The golden ratio in photography can make an image way more interesting that it would normally be without this technique, although it is quite hard to find for a person who only takes pictures for memories and such, the golden ratio can really make your photos look better and way way more interesting (as i have already mentioned). If you are a beginner at photography, the easiest thing to practice the golden ratio with is taking photos of those seashells, or them shells or whatever it is called, Because the golden ratio looks very similar to a seashell.
This is a simple diagram we call the phi grid. It dates back to the 13th century, invented by a man called Leonardo Fibonacci. The grid (or ratio, or rule, however you want to refer it as it has so many names) has many different names such as The Golden Ratio, The Phi Grid, The Divine Proportion or even the Golden Mean! (i'm 1000% sure that there is more by the way). The phi grid is a very advanced method of photography, i would not advise going straight into it, I would master all the other more easier methods of composition before attempting to learn this one. Although this method could quite easily be achieved accidentally, it is really hard to make in a normal image, unless the object you are trying to take a photo of is quite easily changeable (you can change it's shape and position), this method if quite difficult.
Here we see a vey adorable kitty cat, the phi grid (or the golden ratio) method has been used in this photo. The smallest square in the curve is the part where the human eye is the most attracted to (most of the time) it is usually because it has a very different tone of color from the rest of the image, which makes it stand out and therefore it is the most concentrated place of the image, the Golden ratio can also relate to the leading lines method, but in a much much more advanced and more difficult way. The most concentrated part of the image could also be something we do not usually see, ahem.. imagine a naked human.... where would your eye want to go immediately? ..... yeah.....