I'm not sure I quite understand it yet, either.
It's pretty simple, the logic is that in order to make an image that people will find interesting, you need to make it look "different". By that, I mean you want and image that hasn't been taken a million times before. The trick is to try things like a different angle, different light, different composition.
The "Rule of Thirds" works against the natural desire to put the subject of your image "dap-smack" in the center of the image. This desire is probably the #1 producer of "boring" photos. The "rule" to "fix" this is:
1) Take your image and divide it into thirds horizontally and vertically. The end result is a "tic-tac-toe" grid on the image.
2) Ideally, place the object of your photo at one of the four corners of the center box of the tic-tac-toe grid. It will also often "work" if you place the subject along one of the lines of the of the center box of the tic-tac-toe pattern.
Another trick is to "go low" or "go high". "Eye level" photos are another killer of interesting images.
Here's what you did "right", knowingly or not:
1) Interesting angle. Though it was probably taken at your eye level at the moment, most people view the ocean from the shoreline and not a couple inches above the water.
2) Rule of Thirds: Two bonus points... 1: the horizon runs across one of the "thirds" grid line, and 2: your toes are at one of the corners. If you'd placed your toes dead center, you'd have a "dead" image.
3) Grain. I assume your disposable was one of those univeral ones loaded with ISO 800 film. Normally film grain is "bad", but here it make the scene look "artsy".
4) Colors. The gradient blue in the sky, the aqua, and the red nails really work well together.