Rule of Thirds is a technique used like a grid. When a subject is to the left or to the right of the picture, it gives it a little more power in terms of how you view the picture.
When you take a picture like this, you are using Texture. It is when you take a picture and it emphasizes it's shape. When seeing a picture, you could imagine what it would feel like. In this case, a big rock.
Symmetry and Patterns is a technique used for places that are parallel. In here, the water is reflecting the trees and they are parallel to each other.
Strong Subject allows you to fill the whole frame. The main focus is the blue ball and you can see detail of it and really focuses you on that instead of the background.
Selective Focus is similar to Strong Subject except in Selective Focus, there are layers. In the picture above, you can identify "layers" of depth. First are the flowers, then you look back at the house, and all the way back are the mountains.
Repetition is used when multiple objects create a pattern. The objects can vary as long as it doesn't drastically affect the patterns.
Negative Space is the area between and around objects in a photograph.
Leading Lines is some sort of object or thing that leads your eyes to a specific subject. In this case, the field line takes your eyes to travel all the way to the football.
Framing is a technique used when an object surrounds or is in the sides of a photo, and then it shows the bigger picture. This is one of my favorite examples.
Angles is a different way to look at a picture. It changes your perspective from a picture. Whether it is from higher or lower, you have to change the perspective of the viewer.