Lines and shapes are the building blocks of our images. Most everything can be broken down into these core elements. By turning your attention to these pieces of the whole you can improve how you see your compositions. The two photos in this post are essentially a series of rectangles. In the photo above there are lots of horizontal rectangles. From the large concrete rectangles at the bottom, to the small rectangular bricks. Even the window panes and window sill are rectangles. All neatly stacked on top of each other. By seeing these parts of the picture as shapes and not just a brick wall and a window, you can visualize how the elements of a photo fit together, or discover that they're not a good fit at all.
The second photo, in contrast, emphasizes vertical rectangles. There are three primary rectangles: the door and the two sections of wood to the sides. We can then break the door into vertical and horizontal rectangles, from the panels of the door to the mailbox. Now here's a finer point about the awareness of shapes. Notice I cut off the top and bottom of the door. You don't see the rectangle of the entire door. Sure, the door is still a rectangle but since you don't see the top and bottom of the door your attention is pushed "into" the door, where the focus is on the textures and shapes that make up the door. The door as a whole becomes a backdrop that sets off the panels of the door. Being aware of such details enables me to fine-tune the visual balance of my images. To improve how you see things you don't always need your camera: look around as you go about your daily life and mentally break down things into lines and shapes. Over time you'll begin to see these building blocks without thinking about it.